FREQUENCY AGILE Tm,HoYLF LOCAL OSCILLATOR FOR A SCANNING DOPPLER WIND LIDAR IN EARTH ORBIT

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NovaSure 电磁波内膜消化术日志书说明书

Radio Frequency Endometrial AblationSurname: Forename:This log book has been designed specifically by Hologic to clearly identify your training needs and track progress. It aims to record experience, understanding and competence of the NovaSure® endometrial ablation system.The log book has 2 main sections:1. Theory: Most topics will be covered in the theoretical Training Day. When you have addressed each subjectin your reading and tutorials, and feel confident about it, then insert the date in the relevant box.2. Practical: Levels 1-4 represents the expected levels of competence and are to be interpreted as follows:Level 1:Observe NovaSure® being carried outLevel 2:Carry out a NovaSure® under direct supervision (your trainer is present throughout)Level 3:Carry out a NovaSure® under indirect supervision (your trainer need not be scrubbed,but should be immediately available for help and advice)Level 4:Independent competence - no supervision neededPractical training should be undertaken at your own hospital with your trainer. Hologic suggests that you undertake:•3 observed cases to meet Level 1 criteria•5 cases managed under direct supervision to meet Level 2 criteria•5 cases managed under indirect supervision to meet Level 3 criteria•5 cases that you have managed independently to meet Level 4 criteriaThere is also an OSATS for performing NovaSure® – please complete regularly to demonstrate progression of training.Additional CasesAdditional CasesAdditional CasesI can confirm that my trainee is now competent to undertake NovaSure ® independently.I can confirm that is now competent to undertake NovaSure ® independently.Title:Hospital/Facility:Trainer:Signature:Date:Signature:Date:Name:Title:Assessor, please tick the candidate’s performance for each of the following factors:Based on the checklist and the Generic Technical Skills Assessment, Dris competent in all areas included in this OSATS is working towards competenceNeeds further help with:Competent to perform the entire procedure without the need for supervisionSigned:Signed:Date:Signed (trainer): Signed (trainee): Date:Self-Verification of competence is undertaken by assessment against the following statements:These statements are designed to indicate competence to use this item. Responsibility for the use remains with the user, so if you are in any doubt regarding your competence to use the item, you should seek education to bring about improvement. Various methods including self-directed learning, coaching and formal training may be initiated (consider local resources, product operating manual, discussion with colleagues or the appropriate key person in your area).Carry out an initial assessment. Y ou must answer yes to all questions before considering yourself to be competent.If you are not competent, instigate learning and then repeat assessment.I certify that I am aware of my professional responsibility for continuing professional development and I realise that I am accountable for my actions. With this in mind I make the following statement:I require further training before I can use this product in a competent mannerI am competent to use this product without further training:Date:Date:Signature:Signature:Indicate how you plan to meet your learning needs:Keep this form in your personal portfolio or training record. Ensure that your Manager receives a copy of the form and enters details of your competence in their records.Statement©2021 Hologic, Inc. Hologic, The Science of Sure, NovaSure and associated logos are trademarks or registered trademarks of Hologic, Inc. and/or its subsidiaries in the United States and/or other countries. This information is intended for medical professionals and is not intended as a product solicitation or promotion where such activities are prohibited. Because Hologic materials are distributed through websites, eBroadcasts and tradeshows, it is not always possible to control where such materials appear. Forspecificinformationonwhatproductsareavailableforsaleinaparticularcountry,**********************************************************************。

The main frequencies of solar core natural oscillations

a r X i v :a s t r o -p h /0409491v 1 21 S e p 2004The main frequencies of solar core natural oscillationsB.V.VasilievInstitute in Physical-Technical Problems,141980,Dubna,Russiasventa@kafa.crimea.uaPACS:64.30.+i;95.30.-kAbstractThe oscillations of a spherical body consisting of hot electron-nuclear plasma are considered.It is shown that there are two basic modes of oscil-lations.The estimation of the main frequencies of the solar core oscillation gives a satisfactory ﬁt of the calculated spectrum and the measurement data.1Introduction.The main parameters of starcoresThe substance of a star interior exists as hot dense electron-nuclear plasma.In the general case,the equilibrium of a hot plasma in a gravitational ﬁeld can be written as∇P +γg +ρE =0(1)where ∇P is the pressure gradient,γis the mass density and ρis the electric density induced by the gravity in plasma,satisfying4πρ=div E ,(2)−4πGγ=div g .(3)It is conventionally accepted to think that the equilibrium exists at E =0and∇P +γg =0.(4)At that the gradient pressure induces the increasing of the density and thetemperature depthward a star.According to the virial theorem the full energy of star is equal to one half of its gravitational (potential)energy.It means the order of value of the full energyE (E =0)≈−GM 2starwhere M star and R star arethemass and the radius of a star.However,it is possible to see that Eq.(1)can be reduced to another equilibrium conditionγg +ρE =0(6)at ∇P =0.Because of a high plasma density into a star core [1],the signiﬁcant part of a star substance is concentred in its core,and the star energy in the order of value isE (∇P =0)≈−GM 2star4r B e 23Z +1∂n eN,T=0,(9)which allows one to obtain the steady-state value of the density of hot non-relativistic plasmaΘ=16( Z +1)3me 2is the Bohr radius, Z is the averaged charge of nuclei plasmais composed from.The equilibrium conditions give possibility to calculate all main parameters of the star core [1]:the equilibrium temperature:T =10kr B≈2·107( Z +1)K ;(11)2the equilibrium mass of core:M=1.56 10Gm2p 3/2 Z A 2,(12) where M Ch= c2 10Gm2p1/2r B8πR4.(14) It is important to underline that the steady-state parameters of a core are depending only on chemical composition of a star,that is expressed through two variable parameters Z and A/Z .These parameters are unknown apriori. 2The sound speed in a hot plasmaThe pressure of a high temperature plasma is a sum of the plasma pressure (ideal gas pressure)and the pressure of black radiation:P=n e kT+am′ln(kT)3/2n e,(16)where m′=AD(ρ,s)=D(p,s) D(ρ,s)3kT5n e[n e+2a(kT)3]1/2(18)For T=T and n e=Θwe have:a(kT)3Θ=1Finally we obtain:c s= 5π4 1/3( Z +1) c A/Z 1/2cm/s.(20) 3The basic elastic oscillation of a spherical core Star cores consist of a dense high temperature plasma which is a compressible matter.The basic mode of elastic vibrations of a spherical core is related with its radius oscillation.For the description of this type of oscillation,the potential φof displacement velocities v r=∂ψr2∂∂r =−Ω2srsinΩs rc s=Ωs Rc s≈4.49.(25)Taking into account Eq.(20)),the main frequency of the core radial elastic os-cillation isΩs=4.49 10.5r3B AF,mHzA/Z(calculation Eq.(26))10.78ηBootisThe Procion(AαCMi)2——βHydri2 2.022.252.372.472 2.6742 3.022 3.19The Sun=M¨R.(28)dR5From thisω2Θ=3π3/2r B k T3/2r3BΘπ2410(3/2)7α3/2 Gm p Z Z +1 4.5 1/2,(30) whereα=e2ksin(kωΘt).(31) 5The main frequencies of the solar core oscilla-tionThe set of the low frequency oscillations withωΘcan be induced by sound oscillations withΩs.At that displacements obtain the spectrum:u R∼sinΩs t· k=01k sin(Ωs±kωΘ)t,(32)whereξis a coeﬃcient≈1.This spectrum is shown in Fig.1b.The central frequency of experimentally measured distribution of the solar oscillation is approximately equal to[Fig.1a]F⊙≈3.23mHz(33) and the experimentally measured frequency splitting in this spectrum is approx-imately equal tof⊙≈67.5µHz(34) (see Fig.2b).At Z =2and A/Z =5the calculated frequencies of basic modes of oscillations(from Eq.(26)and Eq.(30))areF=Ωs2π=66.0µHz.(35)It is important to note that there are two ways for the core chemical compo-sition determination.Thus chemical parameters Z and A/Z can be obtained byﬁtting at the known frequency of basic oscillation F as it was done above (according to Table1).Another way-to express these parameters through F6and f.The betweenness relation of two this frequencies gives a possibility for a direct determination of averaged parameters of nuclei which the core composed from:4/3−1(36)Z =4.494/3101/310.52/3Fand2.(37)A/Z =37α3r3B4.493f2Using experimentally obtained frequencies(Eq.(33)and Eq.(34)),we have for the solar coreZ ⊙=2.03(38) andA/Z ⊙=4.99.(39) Thus both these ways of determination of chemical parameters give prac-tically identical results that demonstrates the adequacy of our consideration.Author thanks J.Christensen-Dalsgaard(Institut for Fysik og Astronomi, Denmark)and G.Houdek(Institute of Astronomy of Cambridge,UK)for help inﬁnding publications of the measurement data.7Figure1:(a)The measured power spectrum of solar oscillation.The data were obtained from the SOHO/GOLF measurement[5].(b)The calculated spectrum described by Eq.(32)at Z=2and A/Z=5.8Figure2:(a)The power obtained by means ofDoppler velocity measurement the solar disk.The data were obtained from the[6].expanded view of a part of the frequency range.9References[1]Vasiliev B.V.-Nuovo Cimento B,2001,v.116,pp.617-634.[2]Landau L.D.and Lifshits E.M.-Statistical Physics,1980,vol.II,3rd edi-tion,Oxford:Pergamon.[3]Landau L.D.and Lifshits E.M.,-Hydrodynamics,vol.VI,(Addison-Wesley,Reading,Mass)1965.[4]Christensen-Dalsgaard,J.,-Stellar oscillation,Institut for Fysik og As-tronomi,Aarhus Universitet,Denmark,2003[5]Solar Physics,vol.175/2,(http://sohowww.estec.esa.nl/gallery/GOLF)[6]Elsworth,Y.at al.-In Proc.GONG’94Helio-and Astero-seismology fromEarth and Space,eds.Ulrich,R.K.,Rhodes Jr,E.J.and D¨a ppen,W.,Asrto-nomical Society of the Pasiﬁc Conference Series,vol.76,San Fransisco,76, 51-54.10。

翻译

相位噪声信号源，如晶体振荡器，在输出频率附近产生一小部分不利的能量（相位噪声）。

对于通信和雷达这样的性能要求较高系统，晶体振荡器采用的频谱纯度越来越重要。

相位噪声是在频域中测量的，并且被表示为在所需信号给定偏移内1赫兹带宽信号功率与噪声功率的比值。

所需信号的各种偏移量的响应图通常是由三种不同的斜坡组成，对应于振荡器相应三种主要噪声产生机理，如图1所示。

比较接近载波的噪声（区域A ）被称为闪烁FM 噪声; 它的大小主要取决于晶体的质量。

Vectron 已经在4-6 MHz 范围内使用第五泛音的AT 切割晶体或第三泛音SC 切割晶体获得最佳近载波噪声结果。

虽然不是所有的都那么好，优异的近载波噪声性能也可以在10 MHz 段使用第三泛音晶体实现，特别是双旋转型（见第41页双旋转SC 的讨论和IT 切割晶体）。

更高频率的晶体导致更高的近载波噪声，因为他们的低Q 值和更宽的带宽。

图1区域B 的噪声，被称为“1/ F ”的噪音，由半导体活动引起的。

在Vectron 低噪音“L2”的晶体振荡器采用的设计技术将其限制到一个非常低的，微不足道的值。

图1的C 区被称为白噪声或宽带噪声。

在Vectron “L2”晶体振荡器特殊的低噪音电路相对于标准设计做出了巨大的改善（15-20分贝）。

当倍频被用来从一个较低频率晶体达到所需的输出频率，输出信号的相位噪声增大了20log （倍增因子）。

这导致在整个倍频过程中约有6分贝噪音降低，相位噪声（dBc/Hz）载波偏移图1三倍频时有10分贝且十倍频时是20 分贝。

如图2，噪声低层几乎为振荡器采用独立的晶振频率而不采用倍频。

因此，对于低噪声层的应用，一般使用满足长期稳定性的要求最高频率的晶体。

然而，当频率更高的应用特别要求最小化近载波相位噪声，低频率的晶体可能经常有成倍地优势。

这是因为近载波相位噪声性能要远远好于使用频率较高的晶体获得的噪声。

需要注意的是变容二极管和可调节Q 晶体的引入，通常在TCXO 和VCXO 产品中使用，导致比固定频率非补偿晶体振荡器较差的近载波噪声性能。

航天器通信特征和关键技术全文-规范文件-

√ The bandwidth of the uplink is narrower than the bandwidt downlink, there may be one or two orders of magnitude 量级 difference. Because the uplink mainly transmits some comm information of the deep space communication facility设施, the downlink transmits telemetry遥测data, analyzing dat other information, which usually include large amount of information.
√ Because of the Earth‘s rotation自传, when the spacecraf the back of the ground station, the communication interru generated.
5
□Asymmetric channel 非对称信道
●Generally the low-frequency radio waves will be attenuate the absorption吸收of the ionosphere, and the radio wave b critical 临界frequency can be echoed反射by the ionospher
□Communication i s interrupted中断
√ As the link connection is intermittent间断, the deep spac communication faces the interruption problems.

IEEE Std 1159-1995,IEEE Recommended Practice for Monitoring Electric Power Quality

IEEE Std 1159-1995 IEEE Recommended Practice for Monitoring Electric Power QualitySponsorIEEE Standards Coordinating Committee 22 onPower QualityApproved June 14, 1995IEEE Standards BoardAbstract: The monitoring of electric power quality of ac power systems, definitions of power quality terminology, impact of poor power quality on utility and customer equipment, and the measurement of electromagnetic phenomena are covered.Keywords: data interpretation, electric power quality, electromagnetic phenomena, monitoring, power quality definitionsIEEE Standards documents are developed within the Technical Committees of the IEEE Societies and the Standards Coordinating Committees of the IEEE Standards Board. Members of the committees serve voluntarily and without compensation. They are not necessarily members of the Institute. The standards developed within IEEE represent a consensus of the broad expertise on the subject within the Institute as well as those activities outside of IEEE that have expressed an interest in partici-pating in the development of the standard.Use of an IEEE Standard is wholly voluntary. The existence of an IEEE Standard does not imply that there are no other ways to produce, test, measure, purchase, mar-ket, or provide other goods and services related to the scope of the IEEE Standard. Furthermore, the viewpoint expressed at the time a standard is approved and issued is subject to change brought about through developments in the state of the art and com-ments received from users of the standard. Every IEEE Standard is subjected to review at least every Þve years for revision or reafÞrmation. When a document is more than Þve years old and has not been reafÞrmed, it is reasonable to conclude that its contents, although still of some value, do not wholly reßect the present state of the art. Users are cautioned to check to determine that they have the latest edition of any IEEE Standard.Comments for revision of IEEE Standards are welcome from any interested party, regardless of membership afÞliation with IEEE. Suggestions for changes in docu-ments should be in the form of a proposed change of text, together with appropriate supporting comments.Interpretations: Occasionally questions may arise regarding the meaning of portions of standards as they relate to speciÞc applications. When the need for interpretations is brought to the attention of IEEE, the Institute will initiate action to prepare appro-priate responses. Since IEEE Standards represent a consensus of all concerned inter-ests, it is important to ensure that any interpretation has also received the concurrence of a balance of interests. For this reason IEEE and the members of its technical com-mittees are not able to provide an instant response to interpretation requests except in those cases where the matter has previously received formal consideration.Comments on standards and requests for interpretations should be addressed to:Secretary, IEEE Standards Board445 Hoes LaneP.O. Box 1331Piscataway, NJ 08855-1331USAIntroduction(This introduction is not part of IEEE Std 1159-1995, IEEE Recommended Practice for Monitoring Electric Power Quality.)This recommended practice was developed out of an increasing awareness of the difÞculty in comparing results obtained by researchers using different instruments when seeking to characterize the quality of low-voltage power systems. One of the initial goals was to promote more uniformity in the basic algorithms and data reduction methods applied by different instrument manufacturers. This proved difÞcult and was not achieved, given the free market principles under which manufacturers design and market their products. However, consensus was achieved on the contents of this recommended practice, which provides guidance to users of monitoring instruments so that some degree of comparisons might be possible.An important Þrst step was to compile a list of power quality related deÞnitions to ensure that contributing parties would at least speak the same language, and to provide instrument manufacturers with a common base for identifying power quality phenomena. From that starting point, a review of the objectives of moni-toring provides the necessary perspective, leading to a better understanding of the means of monitoringÑthe instruments. The operating principles and the application techniques of the monitoring instruments are described, together with the concerns about interpretation of the monitoring results. Supporting information is provided in a bibliography, and informative annexes address calibration issues.The Working Group on Monitoring Electric Power Quality, which undertook the development of this recom-mended practice, had the following membership:J. Charles Smith, Chair Gil Hensley, SecretaryLarry Ray, Technical EditorMark Andresen Thomas Key John RobertsVladi Basch Jack King Anthony St. JohnRoger Bergeron David Kreiss Marek SamotyjJohn Burnett Fran•ois Martzloff Ron SmithJohn Dalton Alex McEachern Bill StuntzAndrew Dettloff Bill Moncrief John SullivanDave GrifÞth Allen Morinec David VannoyThomas Gruzs Ram Mukherji Marek WaclawlakErich Gunther Richard Nailen Daniel WardMark Kempker David Pileggi Steve WhisenantHarry RauworthIn addition to the working group members, the following people contributed their knowledge and experience to this document:Ed Cantwell Christy Herig Tejindar SinghJohn Curlett Allan Ludbrook Maurice TetreaultHarshad MehtaiiiThe following persons were on the balloting committee:James J. Burke David Kreiss Jacob A. RoizDavid A. Dini Michael Z. Lowenstein Marek SamotyjW. Mack Grady Fran•ois D. Martzloff Ralph M. ShowersDavid P. Hartmann Stephen McCluer J. C. SmithMichael Higgins A. McEachern Robert L. SmithThomas S. Key W. A. Moncrief Daniel J. WardJoseph L. KoepÞnger P. Richman Charles H. WilliamsJohn M. RobertsWhen the IEEE Standards Board approved this standard on June 14, 1995, it had the following membership:E. G. ÒAlÓ Kiener, Chair Donald C. Loughry,Vice ChairAndrew G. Salem,SecretaryGilles A. Baril Richard J. Holleman Marco W. MigliaroClyde R. Camp Jim Isaak Mary Lou PadgettJoseph A. Cannatelli Ben C. Johnson John W. PopeStephen L. Diamond Sonny Kasturi Arthur K. ReillyHarold E. Epstein Lorraine C. Kevra Gary S. RobinsonDonald C. Fleckenstein Ivor N. Knight Ingo RuschJay Forster*Joseph L. KoepÞnger*Chee Kiow TanDonald N. Heirman D. N. ÒJimÓ Logothetis Leonard L. TrippL. Bruce McClung*Member EmeritusAlso included are the following nonvoting IEEE Standards Board liaisons:Satish K. AggarwalRichard B. EngelmanRobert E. HebnerChester C. TaylorRochelle L. SternIEEE Standards Project EditorivContentsCLAUSE PAGE 1.Overview (1)1.1Scope (1)1.2Purpose (2)2.References (2)3.Definitions (2)3.1Terms used in this recommended practice (2)3.2Avoided terms (7)3.3Abbreviations and acronyms (8)4.Power quality phenomena (9)4.1Introduction (9)4.2Electromagnetic compatibility (9)4.3General classification of phenomena (9)4.4Detailed descriptions of phenomena (11)5.Monitoring objectives (24)5.1Introduction (24)5.2Need for monitoring power quality (25)5.3Equipment tolerances and effects of disturbances on equipment (25)5.4Equipment types (25)5.5Effect on equipment by phenomena type (26)6.Measurement instruments (29)6.1Introduction (29)6.2AC voltage measurements (29)6.3AC current measurements (30)6.4Voltage and current considerations (30)6.5Monitoring instruments (31)6.6Instrument power (34)7.Application techniques (35)7.1Safety (35)7.2Monitoring location (38)7.3Equipment connection (41)7.4Monitoring thresholds (43)7.5Monitoring period (46)8.Interpreting power monitoring results (47)8.1Introduction (47)8.2Interpreting data summaries (48)8.3Critical data extraction (49)8.4Interpreting critical events (51)8.5Verifying data interpretation (59)vANNEXES PAGE Annex A Calibration and self testing (informative) (60)A.1Introduction (60)A.2Calibration issues (61)Annex B Bibliography (informative) (63)B.1Definitions and general (63)B.2Susceptibility and symptomsÑvoltage disturbances and harmonics (65)B.3Solutions (65)B.4Existing power quality standards (67)viIEEE Recommended Practice for Monitoring Electric Power Quality1. Overview1.1 ScopeThis recommended practice encompasses the monitoring of electric power quality of single-phase and polyphase ac power systems. As such, it includes consistent descriptions of electromagnetic phenomena occurring on power systems. The document also presents deÞnitions of nominal conditions and of deviations from these nominal conditions, which may originate within the source of supply or load equipment, or from interactions between the source and the load.Brief, generic descriptions of load susceptibility to deviations from nominal conditions are presented to identify which deviations may be of interest. Also, this document presents recommendations for measure-ment techniques, application techniques, and interpretation of monitoring results so that comparable results from monitoring surveys performed with different instruments can be correlated.While there is no implied limitation on the voltage rating of the power system being monitored, signal inputs to the instruments are limited to 1000 Vac rms or less. The frequency ratings of the ac power systems being monitored are in the range of 45Ð450 Hz.Although it is recognized that the instruments may also be used for monitoring dc supply systems or data transmission systems, details of application to these special cases are under consideration and are not included in the scope. It is also recognized that the instruments may perform monitoring functions for envi-ronmental conditions (temperature, humidity, high frequency electromagnetic radiation); however, the scope of this document is limited to conducted electrical parameters derived from voltage or current measure-ments, or both.Finally, the deÞnitions are solely intended to characterize common electromagnetic phenomena to facilitate communication between various sectors of the power quality community. The deÞnitions of electromagnetic phenomena summarized in table 2 are not intended to represent performance standards or equipment toler-ances. Suppliers of electricity may utilize different thresholds for voltage supply, for example, than the ±10% that deÞnes conditions of overvoltage or undervoltage in table 2. Further, sensitive equipment may mal-function due to electromagnetic phenomena not outside the thresholds of the table 2 criteria.1IEEEStd 1159-1995IEEE RECOMMENDED PRACTICE FOR 1.2 PurposeThe purpose of this recommended practice is to direct users in the proper monitoring and data interpretation of electromagnetic phenomena that cause power quality problems. It deÞnes power quality phenomena in order to facilitate communication within the power quality community. This document also forms the con-sensus opinion about safe and acceptable methods for monitoring electric power systems and interpreting the results. It further offers a tutorial on power system disturbances and their common causes.2. ReferencesThis recommended practice shall be used in conjunction with the following publications. When the follow-ing standards are superseded by an approved revision, the revision shall apply.IEC 1000-2-1 (1990), Electromagnetic Compatibility (EMC)ÑPart 2 Environment. Section 1: Description of the environmentÑelectromagnetic environment for low-frequency conducted disturbances and signaling in public power supply systems.1IEC 50(161)(1990), International Electrotechnical V ocabularyÑChapter 161: Electromagnetic Compatibility. IEEE Std 100-1992, IEEE Standard Dictionary of Electrical and Electronic Terms (ANSI).2IEEE Std 1100-1992, IEEE Recommended Practice for Powering and Grounding Sensitive Electronic Equipment (Emerald Book) (ANSI).3. DeÞnitionsThe purpose of this clause is to present concise deÞnitions of words that convey the basic concepts of power quality monitoring. These terms are listed below and are expanded in clause 4. The power quality commu-nity is also pervaded by terms that have no scientiÞc deÞnition. A partial listing of these words is included in 3.2; use of these terms in the power quality community is discouraged. Abbreviations and acronyms that are employed throughout this recommended practice are listed in 3.3.3.1 Terms used in this recommended practiceThe primary sources for terms used are IEEE Std 100-19923 indicated by (a), and IEC 50 (161)(1990) indi-cated by (b). Secondary sources are IEEE Std 1100-1992 indicated by (c), IEC-1000-2-1 (1990) indicated by (d) and UIE -DWG-3-92-G [B16]4. Some referenced deÞnitions have been adapted and modiÞed in order to apply to the context of this recommended practice.3.1.1 accuracy: The freedom from error of a measurement. Generally expressed (perhaps erroneously) as percent inaccuracy. Instrument accuracy is expressed in terms of its uncertaintyÑthe degree of deviation from a known value. An instrument with an uncertainty of 0.1% is 99.9% accurate. At higher accuracy lev-els, uncertainty is typically expressed in parts per million (ppm) rather than as a percentage.1IEC publications are available from IEC Sales Department, Case Postale 131, 3, rue de VarembŽ, CH-1211, Gen•ve 20, Switzerland/ Suisse. IEC publications are also available in the United States from the Sales Department, American National Standards Institute, 11 West 42nd Street, 13th Floor, New York, NY 10036, USA.2IEEE publications are available from the Institute of Electrical and Electronics Engineers, 445 Hoes Lane, P.O. Box 1331, Piscataway, NJ 08855-1331, USA.3Information on references can be found in clause 2.4The numbers in brackets correspond to those bibliographical items listed in annex B.2IEEE MONITORING ELECTRIC POWER QUALITY Std 1159-1995 3.1.2 accuracy ratio: The ratio of an instrumentÕs tolerable error to the uncertainty of the standard used to calibrate it.3.1.3 calibration: Any process used to verify the integrity of a measurement. The process involves compar-ing a measuring instrument to a well defined standard of greater accuracy (a calibrator) to detect any varia-tions from specified performance parameters, and making any needed compensations. The results are then recorded and filed to establish the integrity of the calibrated instrument.3.1.4 common mode voltage: A voltage that appears between current-carrying conductors and ground.b The noise voltage that appears equally and in phase from each current-carrying conductor to ground.c3.1.5 commercial power: Electrical power furnished by the electric power utility company.c3.1.6 coupling: Circuit element or elements, or network, that may be considered common to the input mesh and the output mesh and through which energy may be transferred from one to the other.a3.1.7 current transformer (CT): An instrument transformer intended to have its primary winding con-nected in series with the conductor carrying the current to be measured or controlled.a3.1.8 dip: See: sag.3.1.9 dropout: A loss of equipment operation (discrete data signals) due to noise, sag, or interruption.c3.1.10 dropout voltage: The voltage at which a device fails to operate.c3.1.11 electromagnetic compatibility: The ability of a device, equipment, or system to function satisfacto-rily in its electromagnetic environment without introducing intolerable electromagnetic disturbances to any-thing in that environment.b3.1.12 electromagnetic disturbance: Any electromagnetic phenomena that may degrade the performance of a device, equipment, or system, or adversely affect living or inert matter.b3.1.13 electromagnetic environment: The totality of electromagnetic phenomena existing at a given location.b3.1.14 electromagnetic susceptibility: The inability of a device, equipment, or system to perform without degradation in the presence of an electromagnetic disturbance.NOTEÑSusceptibility is a lack of immunity.b3.1.15 equipment grounding conductor: The conductor used to connect the noncurrent-carrying parts of conduits, raceways, and equipment enclosures to the grounded conductor (neutral) and the grounding elec-trode at the service equipment (main panel) or secondary of a separately derived system (e.g., isolation transformer). See Section 100 in ANSI/NFPA 70-1993 [B2].3.1.16 failure mode: The effect by which failure is observed.a3.1.17 ßicker: Impression of unsteadiness of visual sensation induced by a light stimulus whose luminance or spectral distribution fluctuates with time.b3.1.18 frequency deviation: An increase or decrease in the power frequency. The duration of a frequency deviation can be from several cycles to several hours.c Syn.: power frequency variation.3.1.19 fundamental (component): The component of an order 1 (50 or 60 Hz) of the Fourier series of a periodic quantity.b3IEEEStd 1159-1995IEEE RECOMMENDED PRACTICE FOR 3.1.20 ground: A conducting connection, whether intentional or accidental, by which an electric circuit or piece of equipment is connected to the earth, or to some conducting body of relatively large extent that serves in place of the earth.NOTEÑ It is used for establishing and maintaining the potential of the earth (or of the conducting body) or approxi-mately that potential, on conductors connected to it, and for conducting ground currents to and from earth (or the con-ducting body).a3.1.21 ground loop: In a radial grounding system, an undesired conducting path between two conductive bodies that are already connected to a common (single-point) ground.3.1.22 harmonic (component): A component of order greater than one of the Fourier series of a periodic quantity.b3.1.23 harmonic content: The quantity obtained by subtracting the fundamental component from an alter-nating quantity.a3.1.24 immunity (to a disturbance): The ability of a device, equipment, or system to perform without deg-radation in the presence of an electromagnetic disturbance.b3.1.25 impulse: A pulse that, for a given application, approximates a unit pulse.b When used in relation to the monitoring of power quality, it is preferred to use the term impulsive transient in place of impulse.3.1.26 impulsive transient: A sudden nonpower frequency change in the steady-state condition of voltage or current that is unidirectional in polarity (primarily either positive or negative).3.1.27 instantaneous: A time range from 0.5Ð30 cycles of the power frequency when used to quantify the duration of a short duration variation as a modifier.3.1.28 interharmonic (component): A frequency component of a periodic quantity that is not an integer multiple of the frequency at which the supply system is designed to operate operating (e.g., 50 Hz or 60 Hz).3.1.29 interruption, momentary (power quality monitoring): A type of short duration variation. The complete loss of voltage (< 0.1 pu) on one or more phase conductors for a time period between 0.5 cycles and 3 s.3.1.30 interruption, sustained (electric power systems): Any interruption not classified as a momentary interruption.3.1.31 interruption, temporary (power quality monitoring):A type of short duration variation. The com-plete loss of voltage (< 0.1 pu) on one or more phase conductors for a time period between 3 s and 1 min.3.1.32 isolated ground: An insulated equipment grounding conductor run in the same conduit or raceway as the supply conductors. This conductor may be insulated from the metallic raceway and all ground points throughout its length. It originates at an isolated ground-type receptacle or equipment input terminal block and terminates at the point where neutral and ground are bonded at the power source. See Section 250-74, Exception #4 and Exception in Section 250-75 in ANSI/NFPA 70-1993 [B2].3.1.33 isolation: Separation of one section of a system from undesired influences of other sections.c3.1.34 long duration voltage variation:See: voltage variation, long duration.3.1.35 momentary (power quality monitoring): A time range at the power frequency from 30 cycles to 3 s when used to quantify the duration of a short duration variation as a modifier.4IEEE MONITORING ELECTRIC POWER QUALITY Std 1159-1995 3.1.36 momentary interruption:See: interruption, momentary.3.1.37 noise: Unwanted electrical signals which produce undesirable effects in the circuits of the control systems in which they occur.a (For this document, control systems is intended to include sensitive electronic equipment in total or in part.)3.1.38 nominal voltage (Vn): A nominal value assigned to a circuit or system for the purpose of conve-niently designating its voltage class (as 120/208208/120, 480/277, 600).d3.1.39 nonlinear load: Steady-state electrical load that draws current discontinuously or whose impedance varies throughout the cycle of the input ac voltage waveform.c3.1.40 normal mode voltage: A voltage that appears between or among active circuit conductors, but not between the grounding conductor and the active circuit conductors.3.1.41 notch: A switching (or other) disturbance of the normal power voltage waveform, lasting less than 0.5 cycles, which is initially of opposite polarity than the waveform and is thus subtracted from the normal waveform in terms of the peak value of the disturbance voltage. This includes complete loss of voltage for up to 0.5 cycles [B13].3.1.42 oscillatory transient: A sudden, nonpower frequency change in the steady-state condition of voltage or current that includes both positive or negative polarity value.3.1.43 overvoltage: When used to describe a specific type of long duration variation, refers to a measured voltage having a value greater than the nominal voltage for a period of time greater than 1 min. Typical val-ues are 1.1Ð1.2 pu.3.1.44 phase shift: The displacement in time of one waveform relative to another of the same frequency and harmonic content.c3.1.45 potential transformer (PT): An instrument transformer intended to have its primary winding con-nected in shunt with a power-supply circuit, the voltage of which is to be measured or controlled. Syn.: volt-age transformer.a3.1.46 power disturbance: Any deviation from the nominal value (or from some selected thresholds based on load tolerance) of the input ac power characteristics.c3.1.47 power quality: The concept of powering and grounding sensitive equipment in a manner that is suit-able to the operation of that equipment.cNOTEÑWithin the industry, alternate definitions or interpretations of power quality have been used, reflecting different points of view. Therefore, this definition might not be exclusive, pending development of a broader consensus.3.1.48 precision: Freedom from random error.3.1.49 pulse: An abrupt variation of short duration of a physical an electrical quantity followed by a rapid return to the initial value.3.1.50 random error: Error that is not repeatable, i.e., noise or sensitivity to changing environmental factors. NOTEÑFor most measurements, the random error is small compared to the instrument tolerance.3.1.51 sag: A decrease to between 0.1 and 0.9 pu in rms voltage or current at the power frequency for dura-tions of 0.5 cycle to 1 min. Typical values are 0.1 to 0.9 pu.b See: dip.IEEEStd 1159-1995IEEE RECOMMENDED PRACTICE FOR NOTEÑTo give a numerical value to a sag, the recommended usage is Òa sag to 20%,Ó which means that the line volt-age is reduced down to 20% of the normal value, not reduced by 20%. Using the preposition ÒofÓ (as in Òa sag of 20%,Óor implied by Òa 20% sagÓ) is deprecated.3.1.52 shield: A conductive sheath (usually metallic) normally applied to instrumentation cables, over the insulation of a conductor or conductors, for the purpose of providing means to reduce coupling between the conductors so shielded and other conductors that may be susceptible to, or that may be generating unwanted electrostatic or electromagnetic fields (noise).c3.1.53 shielding: The use of a conducting and/or ferromagnetic barrier between a potentially disturbing noise source and sensitive circuitry. Shields are used to protect cables (data and power) and electronic cir-cuits. They may be in the form of metal barriers, enclosures, or wrappings around source circuits and receiv-ing circuits.c3.1.54 short duration voltage variation:See: voltage variation, short duration.3.1.55 slew rate: Rate of change of ac voltage, expressed in volts per second a quantity such as volts, fre-quency, or temperature.a3.1.56 sustained: When used to quantify the duration of a voltage interruption, refers to the time frame asso-ciated with a long duration variation (i.e., greater than 1 min).3.1.57 swell: An increase in rms voltage or current at the power frequency for durations from 0.5 cycles to 1 min. Typical values are 1.1Ð1.8 pu.3.1.58 systematic error: The portion of error that is repeatable, i.e., zero error, gain or scale error, and lin-earity error.3.1.59 temporary interruption:See: interruption, temporary.3.1.60 tolerance: The allowable variation from a nominal value.3.1.61 total harmonic distortion disturbance level: The level of a given electromagnetic disturbance caused by the superposition of the emission of all pieces of equipment in a given system.b The ratio of the rms of the harmonic content to the rms value of the fundamental quantity, expressed as a percent of the fun-damental [B13].a Syn.: distortion factor.3.1.62 traceability: Ability to compare a calibration device to a standard of even higher accuracy. That stan-dard is compared to another, until eventually a comparison is made to a national standards laboratory. This process is referred to as a chain of traceability.3.1.63 transient: Pertaining to or designating a phenomenon or a quantity that varies between two consecu-tive steady states during a time interval that is short compared to the time scale of interest. A transient can be a unidirectional impulse of either polarity or a damped oscillatory wave with the first peak occurring in either polarity.b3.1.64 undervoltage: A measured voltage having a value less than the nominal voltage for a period of time greater than 1 min when used to describe a specific type of long duration variation, refers to. Typical values are 0.8Ð0.9 pu.3.1.65 voltage change: A variation of the rms or peak value of a voltage between two consecutive levels sustained for definite but unspecified durations.d3.1.66 voltage dip:See: sag.IEEE MONITORING ELECTRIC POWER QUALITY Std 1159-1995 3.1.67 voltage distortion: Any deviation from the nominal sine wave form of the ac line voltage.3.1.68 voltage ßuctuation: A series of voltage changes or a cyclical variation of the voltage envelope.d3.1.69 voltage imbalance (unbalance), polyphase systems: The maximum deviation among the three phases from the average three-phase voltage divided by the average three-phase voltage. The ratio of the neg-ative or zero sequence component to the positive sequence component, usually expressed as a percentage.a3.1.70 voltage interruption: Disappearance of the supply voltage on one or more phases. Usually qualified by an additional term indicating the duration of the interruption (e.g., momentary, temporary, or sustained).3.1.71 voltage regulation: The degree of control or stability of the rms voltage at the load. Often specified in relation to other parameters, such as input-voltage changes, load changes, or temperature changes.c3.1.72 voltage variation, long duration: A variation of the rms value of the voltage from nominal voltage for a time greater than 1 min. Usually further described using a modifier indicating the magnitude of a volt-age variation (e.g., undervoltage, overvoltage, or voltage interruption).3.1.73 voltage variation, short duration: A variation of the rms value of the voltage from nominal voltage for a time greater than 0.5 cycles of the power frequency but less than or equal to 1 minute. Usually further described using a modifier indicating the magnitude of a voltage variation (e.g. sag, swell, or interruption) and possibly a modifier indicating the duration of the variation (e.g., instantaneous, momentary, or temporary).3.1.74 waveform distortion: A steady-state deviation from an ideal sine wave of power frequency princi-pally characterized by the spectral content of the deviation [B13].3.2 Avoided termsThe following terms have a varied history of usage, and some may have speciÞc deÞnitions for other appli-cations. It is an objective of this recommended practice that the following ambiguous words not be used in relation to the measurement of power quality phenomena:blackout frequency shiftblink glitchbrownout (see 4.4.3.2)interruption (when not further qualiÞed)bump outage (see 4.4.3.3)clean ground power surgeclean power raw powercomputer grade ground raw utility powercounterpoise ground shared grounddedicated ground spikedirty ground subcycle outagesdirty power surge (see 4.4.1)wink。

CubaseSX术语英汉对照表

Joystick 控制手柄，操纵杆，摇杆JSS jet servo system 喷射伺服式重低音扬声器系统Jumper 跳线，条形接片Justify 调整Input 输入Indicator 显示器，指示灯INS insert 插入（信号），插入接口INSEL input select 输入选择INST instant 直接的，实时INST institution 建立，设置INST instrument 仪器，乐器Instrument 乐器Insulator 绝缘体INT intake 进入，入口INT intensity 强度，烈度INT interior 内部INT interrupter 断路器Integrated 组合的Integrated amplifier前置-功率放大器，综合功率放大器Intelligate 智能化噪声门Intelligibility 可懂度Interactie 相互作用，人机对话，软拐点Interval 音高差别Integrated 集成的，完全的Intercom 对讲，通话Interconnect 互相联系Inter cut 插播Interface 接口，对话装置Interference 干扰，干涉，串扰Interim 临时的，过渡特征Intermodulation 互调，内调制Intermodulation distortion 交越失真Internal 内存，对讲机Internally 在内部，内存Inter parameter 内部参数Interval 音高差别Interplay 相互作用，内部播放Interval shifter 音歇移相器Intimacy 亲切感Intonation 声调INTRO introduction 介绍，浏览，引入，（乐曲的）前奏INTRO sacn 曲头检索（节目搜索）INTRO sensor 曲头读出器（节目查询）Introskip 内移，内跳ISS insertion test signal 插入切换信号ISS interference suppression switch 干扰抑制开关ITS insertion test signal 插入测试信号IV interval 间隔搜索IV inverter 倒相器IWC interrupted wave 断续波IX index K-LK key 按键Karaoke 卡?OK，无人伴奏乐队KB key board 键盘，按钮Kerr 克耳效应，（可读写光盘）磁光效应Key 键，按键，声调Keyboard 键盘，按钮Key control 键控，变调控制Keyed 键控Key EQ 音调均衡kHz Kiloherts 千赫兹Kikll 清除，消去，抑制，衰减，断开Killer 抑制器，断路器Kit 设定Knee 压限器拐点Knob 按钮，旋钮，调节器KP key pulse 键控脉冲KTV karaoke TV 拌唱电视（节目）KX key 键控Lesion 故障，损害Leslie 列斯利（一种调相效果处理方式）LEV level 电平LEVCON level control 电平控制Level 电平，水平，级LF low frequency 低频，低音LFB local feedback 本机反馈，局部反馈LFE lowfrequency response 低频响应LFO low frequency oscillation 低频振荡信号LGD long delay 长延时LH low high 低噪声高输出LH low noise high output 低噪声高输出磁带L.hall large hall 大厅效果Lift 提升（一种提升地电位的装置）Lift up 升起Labial 唇音L left 左（立体声系统的左声道）L line 线路L link 链路L long 长（时间）LA laser 激光（镭射）Lag 延迟，滞后Lamp 灯，照明灯Land 光盘螺旋道的肩，接地，真地Lap dissolve 慢转换Lapping SW 通断开关Large 大，大型Large hall 大厅混响Larigot 六倍音Laser 激光（镭射）Latency 空转，待机Launching 激励，发射Layer 层叠控制，多音色同步控制LCD liquid crystal display 液晶显示LCR left center right 左中右LD laser vision disc 激光视盘，影碟机LD load 负载LDP input 影碟输入LDTV low definition television低分辨率数字电视LCD projictor 液晶投影机Lead 通道，前置，输入Lead-in 引入线Leak 漏泄Learn 学习LED light emitting deivce 发光辐射器，发光器件LED litht emitting diode 发光二极管（显示）Legato 连奏Length 字长，范围Lento 慢板Light switch 照明开关标盘，指针，索引-NM main 主信道M master 主控M memory 存储器M mix 混频M moderate 适中的M music 音乐Mac manchester auto code 曼切斯特自动码MADI musical audio digital interface 音频数字接口Main 主要的，主线，主通道，电源MAG magnet 磁铁Magnetic tape 磁带Magnetic type recorder 磁带录音机Main 电源，主要的Major chord 大三和弦Make 接通，闭合Makeup 接通，选配Male 插头，插件MAN manual 手动的，手控Manifold technology （音箱）多歧管技术Manipulate 操作，键控MANP 手动穿插Manual 手动的，人工的，手册，说明书March 进行曲Margin （电平）余量Mark 标志，符号，标记Mash 压低，碾碎Masking 掩蔽Master 总音量控制，调音台，主盘，标准的，主的，总路MAR Matrix 矩阵，调音台矩阵（M），编组Match 匹配，适配，配对Matrix quad system 矩阵四声道立体声系统MAX maximum 最大，最大值MB megabytes 兆字节Mb/s megabytes per second 兆字节/秒MC manual control 手控，手动控制MCH multiple chorus 多路合唱MCR multiple cjhannel amplification reverberation多路混响增强MD mini disc 光磁盘唱机，小型录放唱盘MD moving coil 动圈式MDL modulation delay 调制延时MEAS measure 测量，范围，测试Measure 乐曲的，小节Meas edit 小结编?MECH mechanism 机械装置MED medium 适中，中间（挡位）Medley 混合Mega bass 超重低音MEM memory 存储器，存储，记忆Member 部件，成员Menu 菜单，目录，表格MEQ mono equalizer 单声道均衡器Merge 合并，汇总，融合Meridian 顶点的，峰值Measure 小结Megaphone 喇叭筒Mel 美（音调单位）Menu 菜单，节目表Message 通信，联系Metal 金属（效果声）Metal tape 金属磁带Meter 电平表，表头，仪表Metronome 节拍器MF matched filter 匹配滤波器MF maveform 波形MF middle frequency 中频，中音MFL multiple flange 多层法兰（镶边）效果MFT multiplprogramming with a fixed number of tasks 任务数量固定的多通道程序设计MIC micro 微米MIC microphone 话筒，麦克风，传声器Michcho level 话筒混响电平Micro monitor amp 微音监听放大器MICROVERB microcomputer reverb 微处理机混响MID middle 中间的，中部的，中音，中频MIDI music instrument digital interface电子乐器数字接口MIN minimum 最小，最小值MIN minute 分钟MIND master integrated network deviceMultiple channel 多通道Multiple effects 综合效果处理装置Multiple jack 多眼插座Multisound ?始音色MUPO maximum undistorted power output最大不失真输出功率MUSE multiple sub-Nyquist sompling encoding多重奈奎斯特取样编码MIDI 格式文件MIDI 信息，全过程N normal 正常，普通，标准N negative 阴极，负极Q-RQ quality factor 品质因数，Q值，频带宽度QD quadrant 象限QD quick disconnect 迅速断开Quack 嘈杂声QUAD quadriphonic 四声道立体声Quadrature 正交，90度相位差，精调Quality 音质，声音QUANT quantitative 定量的QUANT quantize 量化，数字化Quantizing 量化Quartz synthesized FM/AM digital tuner石英晶体频率合成式调频/调幅数字调谐器Quartz PLL frequency synthesizer 晶体销相环频率Quaver 八分音符Quench 断开，抑制Quint 五度，次三倍音Quiver 颤动声Ribbon microphone 铝带话筒，压力带话筒Richness 丰满度Rhythm 节奏Right 右声道，垂直的，适当的Ring 环，大三芯环端，冷端接点，振铃Ring mode 声反馈临界振铃振荡现象Rit 渐慢RF radio frequency 射频，高频RM regular matrix record 正规矩阵式四路唱片RM ring modulation 环形调制器RMD fing mode decoupling （音箱）振铃退耦技术RMR room reverb 房间混响RMS random music sensor 随机音乐探测器Rms root mean square 有效值RND random 随机的RNG ring 振铃Roadrack 专业器材架Rock 摇滚乐、摇滚乐音响效果Rod antenna ?杆天线RODS reverberation on demand system 混响请求系统Rolloff 高低频规律性衰减，滚降ROM read only memory 只读存储器Room 房间Rose 接线盒Rotary 旋转RT60 Reverberation time 混响时间Rough 粗的，粗糙的，近似的Routing 混合母线选择RP record playback 录放RP repeater 增音转发器RPLC replace 替换RSS Roland sound space processing system罗兰声空间处理系统RT rael time 实时分析RT recovery time 恢复时间RT return 返回RTA real time analyzer 实时分析（仪），频谱分析（仪）RTS real time simulator 实时模拟RTS real time system 实时系统RTY rotary 旋转（扬声器）Rubber corrugated ri loudspeaker 橡皮边扬声器Ruby stylus 红宝石唱针Rumba 伦巴Rumble （低频）隆隆声RV rendezvous 会聚点RVS reverse shift 反向移动RZ return to zero 归零Reversal 反相，相反，反转，改变极性Reverse 回复，?转，反混响Revert 复?，返回Review 检查，复查，重复Revolve 旋转，?环REW rewind 快速倒带RF radio frequency 射频RF reception fair 接收情况良好RFI RF interface 射频接口RFI RF interferece 射频干扰Revcolor 混响染色声RPS direct program 直接节目搜寻，卡?OK搜索R(RD)radio 射频R(RD)read 读取R receiver 接收机R register 寄存器R right 右声道Rack 机架，支架，机柜，规定宽度，震动声Radiation 辐射Radio 无线电，惦音机，射频Ram random access memory 随机存储器RAM 填入，装入RAN random 随机的，任意的，无规则的Range 范围，最大提衰量，幅度Rate 比率，速率，变化率，频率Ratio 压缩比，扩展比，比，系数RCA radio corporation of America 美国无线电公司RCA jack 莲花接口R-CH 右声道R-DA T rotary head-DA T 旋转磁头式数字录音机RE rack earth 外壳接地RE reset 复位RE right end 右端Reactance 电抗Readjustment 重调Ready 预备，准备完毕Rear 背面，后部，后置REC recording 录音，记录，录制Recall 招回，调出，重录Receiver 接受机，接受器Recharge 再充电Record 记录，录制，唱片Recorder 录音机Recovery 恢复，复?Red 红色Redo 再执行操作Reduce 减少，降低，缩小Reduction 压缩，衰减，形成Reecho 回声REF Reference 说明书，参考，基准，定位REF Reflection 反射Refraction 折射Refresh 恢复REG register 寄存器REG regulate 控制，校准，调节REGEN regeneration 再生（混响声阵形成方式），正反馈Rehearsal 排练，预演Reject 除去，滤去Rejection 抑制Reinforcement 扩声Relay 继电器，重放，转放Release 恢复时间，释放，断路器Rename 改名，命名Remain 保持，剩余REM remote 遥控的，遥远的，远距离的REM removable 可拆装的REM remove 除去Remain 余量，状态保持Renumber 重写号码REP repeat 重复，反复，重放Repeat mode 双面反复放音（录音机）Replacing 替换，置换，复位REQ room equalizer 房间均衡器Reset 复位，恢复，归零，重复，重新安装Resolution 分辨率，分析Resonance 共振，回声RESP response 响应，特性曲线，回答Resistance 阻抗Resister 电阻Resonance 共鸣，谐振Rest 休止符，静止，停止Restraint 抑制，限制器RET return 返回，回送REV reverse 颠倒，反转REV reverberation 混响，残响Reverb depth control 混响深度控制RIAA recording industry association of America美国录音工业?会S-TSAF Safety 安全装置，保险装置，保护装置Safeguard by 防护器SALT symmetry air load technique 对称空气负载技术Samba 桑巴Sample 声音信号样品，采样，取样，抽样Sampling 抽样，脉冲调制SAP second audio program 第二套音频节目SA T saturate 饱和效果处理Save 贮存Save 存储，保存Saxophoneb 萨克司管Saxophome 顶馈直线天线SC set clock 置位时钟SC sigmal control 信号控制SC subcarrier 副载波SC system controller 系统控制器SC scan 扫描Scale 音阶，刻度尺标Scale unit 标度单位，分频器Scan 搜索，记录，扫描Scar 激光唱片上的缺陷SCART connector欧洲标准21脚A V接口Scattering 散射Scene 实况，场面SCH search 搜索，寻找Scheme 设计图，?理图SCMS serial copy management system 成套复制管理系统Screw 螺丝钉Scrollback 回找SCH stereochrous 立体声合唱Schmidt trigger 施密特触发器Scintillation 闪烁，调制引起的载频变化SCMS successive copy manage system连续复制管理系统（DA T设备中防止多次转录节目的系统）Scoop 戽斗，收集器Scope 范围，显示器Scoring 音乐录音SCR signal to clutter ratio 信噪比SCR silicon controlled rectifier 晶闸管整流器Scraper 刮声器Screen 屏蔽SD space division 空间分布S-DA T stationary head DA T 固定磁头DA T机SDDS sony dynamic digital sound 索尼动态数字环绕声系统SDI standard data interface 标准数据接口SDLC synchronous data link control 同步数据链控制器SE single end 单端的SE sound effect 音响效果SE storage element 存储元件SE support equipment 支援设备SEA soond effect amplifier 音响效果放大器SEA special effects amplifier 特殊效果放大器Search 搜索，扫描Searcher 扫描器SEC Second 秒，第二SECAM sequential color and memory 调频行轮换彩色制式Section 单元，环节Sectoral horm 扇形号筒Security 保险，加锁SED system effectiveness demonstration 系统效果演示Seek 搜索SEL selector 选择装置，寻线器，转换开关Select 选择Selectivity （收音机）选择性Minitrim 微调Minitrue 微机调整Minor chord 小三和弦Mismatch 失配Mistermination 终端失配MIX 混合，音量比例调节Mixer 调音台，混音器MM moving magnet 动磁式MNTR monitor 监控器MNOS metallic nitrogen - oxide semiconductor 金属氮氧化物半导体MO magneto optical 可抹可录型光盘MOC magnet oscillator circuit 主振荡电路MOD mode 状态，方式，模式MOD model 型号，样式，模型，典型的MOD modulation 调制Mode 状态，（乐曲的）调式Mode select 方式选择Mush 噪声干扰，分谐波Mush area 不良接收区Music 音乐，乐曲Music center 音乐中心，组合音响Music conductor 音乐控制器MUT mute 静音，埔簦?肷?刂?Muting 抑制，消除Multiple 复合的，多项的，多重的MV mean value 平均值MV multivibrator 多谐振荡器MW medium wave 中波MXE mono exciter 单声道激励器MXR mixer 混频器Name 名称，命名Natural 自然的，天然的，固有的Naught 零，无价值NC network controller 网络控制器NC numberical control 数字控制NC needle chatter 唱针噪声Nazard 三倍音Near field 近场NEG negative 负，阴（极）NEMO 实况转播NEP noise equivalent power 噪声等效功率News 人声广播音响效果，新闻Next 下一个，唱片跳回下曲键NF NFB negative feedback 负反馈NG no go 不通，不工作NG noise generator 噪声发生器Ni-Cd nickel-cadmium 镍镉充电电池NICAM near instantaneous companded audio multiplex准瞬时压扩声音多路复用，电视丽音，数字多路伴音系统NIL 零点Noise 噪音Noise gate 噪声门，选通器Noise suppressor 噪声抑制器NOM nominal 标称的，额定的Non-direction 全向的，无指向性的Nonieme 九倍音NOP no operation 无操作指令NOR(NORM) normal 普通的，标准的，正常的，常规的NORM 平均值Normal frequency 简正（共振）频率Notch 触点Note 符号，注释，音调，音律，记录Notice 注意事项，简介NO number 数字，号码NR noise ratio 噪声比NR noise reduction 降噪，噪声消除NR number 数字，编号NAB national association of broadcasters国家广播工作者?会NTSC national television system committee（美国）国家电视系统委员会，正交平衡调幅制彩色电视制式Null 空位，无效的NV noise variance 噪声方差NVT network virtual terminal 网络虚拟终段MODEM modulator demodulator 调制解调器Moderato 中速Modifier 调节器Modify 修改，调试，摩机，限定Modulator 调制器Module 模块，组件，因数，程序片MOL maximum output level 最大输出电平MON monitor 监听，监视器MONI 监听，调音师Monkey chatter 串音，邻频干扰，交叉失真Mono 单声道，单一Monopit 单声变调Motor cue 换机信号，切换信号MOS metal-oxide semiconductor 金属氧化物半导体Motor 马达，电机Movie theater 影剧院Moviola 声?剪?机Moving-iron loudspeaker 舌簧扬声器MPEG motion picture coding experts group活动图像编码专家组，数字声像信息压缩标准MPF master pre feed 主控前馈送MPH multiple phaser 多级移相器MPO maximum power output 最大输出功率MPO music power output 音乐输出功率MPR master pre return 主控前返回MPS main power switch 主电源开关MPS manual phase shifter 手控相移器MPS microphone power supply 话筒电源MPS microprocessor system 多用途取样系统MPX multiplex 多路传输，多次重复使用，多路转换，复合MPX multiplexer 多路转换器，多路调制器MPX VCO 多路解调压控振荡MQSS music quick select system 快速音乐选择系统MR memory read 存储器读出MS manual search 手动检索MS middle side 一种迭合录音技术MS(MSEC) millisecond 毫秒MSSS multi space ound system 多维空间声系统MST(MSTR) master 主控MSW microswitch 微动开关MT multi track 多轨MTD multiple delay 多次延时MTR magnetic tape redorder 磁带记录器MTR micro-wave transmission 微波传输MTR motor 电动机MTS multi-channel television sound 多声道电视伴音MTV music TV 音乐电视（节目）MUF maximum usable frequency 最高可用频率MULT multiplier 倍增器，光电倍增管Multi 并联的，多路系统Multidimention control 声场展宽控制，多维控制Multiband 多频段Multi-echo 多重回声Multi plex 多路传声Multitap 转接，（多插头）插座Multiple channel 多通道Multiple effects 综合效果处理装置Multiple jack 多眼插座Multisound ?始音色MUPO maximum undistorted power output最大不失真输出功率MUSE multiple sub-Nyquist sompling encoding多重奈奎斯特取样编码MIDI 格式文件MIDI 信息，全过程N normal 正常，普通，标准N negative 阴极，负极Natural 自然的，天然的，固有的Naught 零，无价值NC network controller 网络控制器NC numberical control 数字控制NC needle chatter 唱针噪声Nazard 三倍音Near field 近场NEG negative 负，阴（极）NEMO 实况转播NEP noise equivalent power 噪声等效功率News 人声广播音响效果，新闻Next 下一个，唱片跳回下曲键NF NFB negative feedback 负反馈NG no go 不通，不工作NG noise generator 噪声发生器Ni-Cd nickel-cadmium 镍镉充电电池NICAM near instantaneous companded audio multiplex准瞬时压扩声音多路复用，电视丽音，数字多路伴音系统NIL 零点Noise 噪音Noise gate 噪声门，选通器Noise suppressor 噪声抑制器NOM nominal 标称的，额定的Non-direction 全向的，无指向性的Nonieme 九倍音NOP no operation 无操作指令NOR(NORM) normal 普通的，标准的，正常的，常规的NORM 平均值Normal frequency 简正（共振）频率Notch 触点Note 符号，注释，音调，音律，记录Notice 注意事项，简介NO number 数字，号码NR noise ratio 噪声比NR noise reduction 降噪，噪声消除NR number 数字，编号NAB national association of broadcasters国家广播工作者?会NTSC national television system committee（美国）国家电视系统委员会，正交平衡调幅制彩色电视制式Null 空位，无效的NV noise variance 噪声方差NVT network virtual terminal 网络虚拟终段MODEM modulator demodulator 调制解调器Moderato 中速Modifier 调节器Modify 修改，调试，摩机，限定Modulator 调制器Module 模块，组件，因数，程序片MOL maximum output level 最大输出电平MON monitor 监听，监视器MONI 监听，调音师Monkey chatter 串音，邻频干扰，交叉失真Mono 单声道，单一Monopit 单声变调Motor cue 换机信号，切换信号MOS metal-oxide semiconductor 金属氧化物半导体Motor 马达，电机Movie theater 影剧院Moviola 声?剪?机Moving-iron loudspeaker 舌簧扬声器MPEG motion picture coding experts group活动图像编码专家组，数字声像信息压缩标准MPF master pre feed 主控前馈送MPH multiple phaser 多级移相器MPO maximum power output 最大输出功率MPO music power output 音乐输出功率MPR master pre return 主控前返回MPS main power switch 主电源开关MPS manual phase shifter 手控相移器MPS microphone power supply 话筒电源MPS microprocessor system 多用途取样系统MPX multiplex 多路传输，多次重复使用，多路转换，复合MPX multiplexer 多路转换器，多路调制器MPX VCO 多路解调压控振荡MQSS music quick select system 快速音乐选择系统MR memory read 存储器读出MS manual search 手动检索MS middle side 一种迭合录音技术MS(MSEC) millisecond 毫秒MSSS multi space ound system 多维空间声系统MST(MSTR) master 主控MSW microswitch 微动开关MT multi track 多轨MTD multiple delay 多次延时MTR magnetic tape redorder 磁带记录器MTR micro-wave transmission 微波传输MTR motor 电动机MTS multi-channel television sound 多声道电视伴音MTV music TV 音乐电视（节目）MUF maximum usable frequency 最高可用频率MULT multiplier 倍增器，光电倍增管Multi 并联的，多路系统Multidimention control 声场展宽控制，多维控制Multiband 多频段Multi-echo 多重回声Multi plex 多路传声Multitap 转接，（多插头）插座。

JBL AW566高功率轻量级2路全范围扬声器系统说明书

Key Features:᭤Weather-Resistant, All Fiberglass Enclosure᭤60° x 60° Coverage᭤ 2265H Differential Drive®Low-Frequency Driver᭤ 2432H High Frequency Compression Driver᭤Large PT™ Progressive Transition waveguide for excellent pattern control and low distortion᭤Available in Gray and Black ﬁnish᭤400 W, 70/100V Transformer Included ᭤U-type Mounting Bracket Included Applications:᭤Sports Facilities᭤Themed Entertainment Venues᭤Outdoor Entertainment Centers᭤Cruise Ships᭤Water ParksThe AW566 is a high power, lightweight, 2-way, full-range loudspeaker system comprised of the JBL Differential Drive dual voice coil and dual magnetic gap 2265H 380mm (15 in) low-frequency driver and 2432H high-frequency 38 mm (1.5in) exit, 75 mm (3 in) voice-coil compression driver. The large format Progressive Transition wave-guide provides excellent 60° x 60° coverage. The loudspeaker system can used in either the vertical or horizontal orientation. The enclosure is constructed of multilayer glass composite and is heavily braced to maximize low-frequency performance. The 16-gauge stainless steel grille, backed with open cell foam and stainless steel mesh, provides excellent protection in the harshest environments. The system is equipped with a 400 W 70/100V transformer.A corrosion-resistant extra-thick zinc-plated polyester powder coated U-type mounting bracket is included.The AW566 is part of JBL’s AE Series, a versatile family of loudspeakers intended for a wide variety of applications.Speciﬁcations:System:Frequency Range (-10 dB):35 Hz – 20 kHzFrequency Response (±3 dB):54 Hz – 18 kHzCoverage Pattern:60° x 60°, rotatable waveguideDirectivity Factor (Q):15.8Directivity Index (DI):12 dBCrossover Frequency: 1.1 kHzLong-Term System Power Rating (IEC):600 W (2400 W peak), 100 hrsMaximum SPL:128 dB-SPL cont avg (134 dB peak)System Sensitivity (1W @ 1m):100 dB SPL70V/100V Transformer Taps:70V: 400 W, 200 W, 100W100V: 400W, 200WTransducers:Low Frequency Driver: 1 x JBL 2265H 380 mm (15 in) Differential Drive driver with 75 mm(3 in) dual voice coilNominal Impedance:8 ohmsSensitivity(1W @ 1m, 98 dB SPLwithin operational band):High Frequency Driver:JBL 2432H, 38 mm (1.5 in) exit compression driver, 75 mm (3 in) voice coil Nominal Impedance:8 ohmsSensitivity(1W @ 1m):113 dB SPLWaveguide:PT-H66HF-1Physical:Enclosure:Hand-Laminated Fiberglass, gray gelcoat (similar to Pantone 420C),available in black (-BK)Suspension Attachment: 2 x M10 for Included U-Bracket, 2 x M6 for aiming stabilization,1x M10 on rear for safety.Grille:Three layer grille assemblies consisting of 16-gauge powder coatedstainless steel, backed with open cell foam and stainless steel mesh.Input Connector:CE-compliant covered barrier strip terminals. Barrier terminals acceptup to 5.2 sq mm (10 AWG) wire or max width 9 mm (.375 in) spadelugs.Environmental Speciﬁcations:IP56 per IEC 529Dimensions (H x W x D in 485 x 810 x 478 mmhorizontal cabinet orientation):(19.1 x 31.9 x 18.8 in)Net Weight:28.3 kg (62.5 lb)IEC standard, full bandwidth pink noise with 6 dB crest factor, 100 hours.Calculated based on power rating and sensitivity, exclusive of power compression.Anechoic sensitivity in free ﬁeld, no additional sensitivity gain from boundary loading.JBL continually engages in research related to product improvement. Changes introduced into existing products without notice are an expression of that philosophy.Professional SeriesAW566High Power 2-Way All Weather Loudspeakerwith 1 x 15" LF & Rotatable Horn᭤AW566 High Power 2-Way All Weather Loudspeaker with 1 x 15" LF & Rotatable HornHorizontal 1/3 Octave Polars᭤AW566 High Power 2-Way All Weather Loudspeaker with 1 x 15" LF & Rotatable HornVertical 1/3 Octave Polars5017361SS AW566CRP09/12 JBL Professional8500 Balboa Boulevard, P.O. Box 2200Northridge, California 91329 U.S.A.© Copyright 2012 JBL Professional。

陶瓷电影实验室电压放大器（第一版）说明书

FEATURESWide Dynamic RangeCharge and Voltage Modes Response to 0.1HzActive HP and LP FiltersAPPLICATIONSLow Frequency Dynamic Strain Pyroelectric SignalsAudio-band and Acoustic Signals Machine VibrationPiezo Cable and Traffic Sensor InterfacePIEZO FILM LAB AMPLIFIERSPECIFICATIONSCharge or Voltage Mode Operation BNC Input and Output0.01 to 1000 mV/pC Sensitivity Range in ChargeMode1M to 1G Input Resistance, -40 to 40dB Gain inVoltage ModeMulti-Pole, Low-Pass and High-Pass Filtering with-3dB Frequencies Ranging from 0.1Hz to 100kHz Internal Battery (2 x 9V) or external 24VDC PowerSupply OperationThe Piezo Film Lab Amplifier is a versatilepreamplifier for use with piezoelectric sensors. The electric signal from the piezo film is generated within the electrodes of a capacitor. It is important to arrange an input that controls the rate of charge leakage appropriately for the application. Simply connecting a piezo film element to the input of an oscilloscope will usually create a high-pass filter that removes any low frequency content of the original piezo signal, and this can lead to disappointment or incorrect evaluation of the material's true potential. This has led MEAS to develop a new low-cost Piezo Film Lab Amp, specifically aimed at developers and engineers exploring the material. Both first-time users and seasoned professionals will benefit from the wide range of sensitivity adjustment in either voltage or charge modes, and the functionality of the high- and low-pass filters.PERFORMANCE SPECIFICATIONSELECTRICALSupply Voltage Internal 2 x 9 V Battery or External 24 VDC (using the supplied 100-240 VAC50/60 Hz power supply unit)Max Input Voltage 30 VMax Linear Output Swing ±4 V (battery), ±5 V (ext)Voltage Mode:Input Resistor Values 1M, 10M, 100M, 1G ΩGain 0 to +40 dB in 10 dB Increments with -40 dB SwitchNoise 30 mV rms (0.20 V pp) typ, 1 Hz to 100 kHz, 1 GΩ Input, +40dB (lower on batterypower)Charge Mode:Feedback Capacitor Values 100pF, 1nF, 10nF, 100nFSensitivity Range 0.01 to 1000 mV/pCNoise 20 mV rms (0.13 V pp) typ, 1 Hz to 100 kHz, 100pF, +40 dB Gain (lower onbattery power)ENVIRONMENTALOperating Temperature 0 to 50°COperating Humidity 5 to 95% RH Non-CondensingSurvival Temperature -20°C to +60°C, Power OffLinearity <1%DESCRIPTION OF CONTROLSMode Selector SwitchThe setting of this switch determines whether the amplifier is functioning in “charge mode” or “voltage mode.” In charge mode, the input appears like a short-circuit sensor and all charge that is generated by the sensor goes into the input and appears on a feedback capacitor within an op-amp circuit. In “voltage mode,” the input appears like an open circuit and no charge flows. The settings of the various input and filter controls then modify the actual performance in either setting.Feedback Capacitance Selector (charge mode)When the amplifier is operating in charge mode, this control changes the sensitivity of the initial amplifier stage. In typical use, it will be set to the value closest to the sensor under test. Selecting a feedback capacitance lower than that of the sensor will create further apparent gain, while selecting a higher feedback capacitance will reduce overall gain. A quantity of charge applied to the input numerically equal to the feedback capacitance value (for example, 100 pC of charge, with 100 pF setting of feedback capacitance) will generate one volt from the initial stage, before further modification by the filters and gain control.Input Impedance Selector (voltage mode)When the amplifier is operating in voltage mode, this control changes the electrical resistance seen at the input of the amplifier. For a given value of sensor capacitance (C), different values of input resistance (R) create different low-frequency response characteristics. The simple RC filter network forms a high-pass filter, which operates independently from the low frequency selector switch. The influence of this impedance selector must therefore beconsidered separately from the low frequency selector (see Appendix B).Input Attenuator Switch (voltage mode)This switch allows the input signal to be attenuated by 40 dB (linear factor of 100), when the amplifier is operating in voltage mode. This can be useful in cases where the open-circuit voltage being monitored is very high, and would cause the output voltage to clip. The setting of this switch does not affect the input impedance seen by the sensor.Low Frequency SelectorThe function of this control is to apply a multi-pole high-pass filter to the signal. Frequencies below the selected limit will be progressively attenuated. In charge mode operation, the signal will be -3 dB down (or approximately 0.7 X) at the selected frequency. In voltage mode, the influence of the RC filter must also be considered (see Input Impedance Selector). Reducing the low-frequency content of a signal may be useful when the signals of interest are relatively high in frequency and low in amplitude.High Frequency SelectorThis control applies a multi-pole low-pass filter to the signal. It can be used in conjunction with the Low Frequency selector to form a band-pass filter, where noise outside a selected band of frequency can be strongly attenuated.Gain SelectorThe purpose of this control is to allow selection of a final gain to be applied to the output of the filter stages. Selecting "0 dB" in voltage mode means that the overall gain of the amplifier is zero dB (linear 1X), when the Input Attenuator is also set to "0 dB". The gain is adjustable in 10 dB steps up to 40 dB (linear 100 X).APPENDIXPower IndicatorThe green power indicator LED lights when the power switch is switched to "1" (ON position), using either the internal batteries or when the external 24 V power supply is connected.Batt LowThe red low battery LED lights when the voltage of the internal batteries falls below approximetly 8 V. When the battery power is no longer sufficient for correct operation, neither "Power" nor "Batt Low" will be illuminated when power switch is switched to "I".Battery CompartmentsThe battery compartments are accessible from the rear panel. To open a compartment, the battery tray should be lifted up slightly, then pulled outwards. Batteries can be left in the amplifier while it is being operated on external power.External Power InputJust below the battery compartments lies the input connector for 24 VDC (center pin +). Use only the power supply provided with the amplifier.Power SwitchThis switches power (from internal batteries or from external 24 VDC supply) to the amplifier on or off. To conserve battery life, power should be switched off when unit is not in use.Input BNCSignal input (for either voltage mode or charge mode operation) should be connected to the Input BNC. Input voltage should not exceed 30 V, and this voltage should not appear across a sensor capacitance in excess of 100 nF. The input adds approx 50 pF shunt capacitance, which must be borne in mind when calculating RC filter frequencies for low-value sensor capacitance in voltage mode.Output BNCImpedance of 50 Ω max. The output of the amplifier is intended to drive theinput of an oscilloscope, signal analyzer, or data acquisition system.Appendix A: Filter response plotsUpper Limiting Frequency Control-60-50-40-30-20-1010110100100010000100000Frequency (Hz)M a g n i t u d e (d B )Lower Limiting Frequency Control-60-50-40-30-20-10100.010.1110100100010000Frequency (Hz)M a g n i t u d e (d B )Appendix B: Influence of Input Impedance selectionon low frequency response (voltage mode)The table below shows the theoretical -3 dB frequency (in Hz) of the high-pass filter that is formed when a sensor of capacitance listed in first column is connected to the specified input impedance.1 M 10 M 100 M 1 G100 p 1592 159 16 1.6220 p 723 72 7.2 0.72470 p 339 34 3.4 0.341 n 159 16 1.6 0.162.2 n 72 7.2 0.72 0.0724.7 n 34 3.4 0.34 0.03410 n 16 1.6 0.16 0.01622 n 7.2 0.72 0.072 0.007247 n 3.4 0.34 0.034 0.0034100 n 1.6 0.16 0.016 0.0016Note: the shaded cells have a -3 dB frequency that is below the range of the Low Frequency Selector, and in this case, the Low frequency Selector will determine the performance. In the case of the unshaded cells, the low frequency limit will be determined either by the Low Frequency selector, or by the data above, whichever is the higher.INCLUDED IN PACKAGE2) Power Supply:Input: 100-240VAC, 50/60Hz, 1.8AOutput: 24VDC 1AConnector: IEC 60320 C14 (inlet)3) Power Supply Cable/PlugMUST BE ORDERED SEPARATLYConnector: IEC 60320 C13Regional Versions Available:1007232-1 - Power Supply Plug, EU1007232-2 - Power Supply Plug, UK1007232-3 - Power Supply Plug, USA1007232-4 - Power Supply Plug, Japan4) Accessoriesa) 2 x 9V Batteries, Type 1604A(6LF22/6LR61/MN1604), Mercury andCadmium Freeb) Piezo Sensor (modified SDT1-028K),p/n 1-1000288-1, 1m Shielded Cable, BNC Connectorc) BNC “Tee” adapterd) 2 x BNC Cable, 0.58m Nominal, Bare End/sensorsolutionsMeasurement Specialties, Inc., a TE Connectivity company.Measurement Specialties, TE Connectivity, TE Connectivity (logo) and EVERY CONNECTION COUNTS are trademarks. 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ENSEMBLE EMPIRICAL MODE DECOMPOSITION-A NOISE ASSISTED DATA ANALYSIS METHOD

July 24,200813:6WSPC/244-AADA 00004Advances in Adaptive Data Analysis 1Vol.1,No.1(2008)1–41c World Scientiﬁc Publishing Company 3ENSEMBLE EMPIRICAL MODE DECOMPOSITION:A NOISE ASSISTED DATA ANALYSIS METHOD 5ZHAOHUA WU ∗and NORDEN E.HUANG †∗Center for Ocean–Land–Atmosphere Studies 74041Powder Mill Road,Suite 302Calverton,MD 20705,USA 9†Research Center for Adaptive Data Analysis National Central University 11300Jhongda Road,Chungli,Taiwan 32001A new Ensemble Empirical Mode Decomposition (EEMD)is presented.This new 13approach consists of sifting an ensemble of white noise-added signal and treats the mean as the ﬁnal true result.Finite,not inﬁnitesimal,amplitude white noise is necessary to 15force the ensemble to exhaust all possible solutions in the sifting process,thus mak-ing the diﬀerent scale signals to collate in the proper intrinsic mode functions (IMF)17dictated by the dyadic ﬁlter banks.As the EMD is a time–space analysis method,the white noise is averaged out with suﬃcient number of trials;the only persistent part 19that survives the averaging process is the signal,which is then treated as the true and more physical meaningful answer.The eﬀect of the added white noise is to provide a 21uniform reference frame in the time–frequency space;therefore,the added noise collates the portion of the signal of comparable scale in one IMF.With this ensemble mean,one 23can separate scales naturally without any a priori subjective criterion selection as in the intermittence test for the original EMD algorithm.This new approach utilizes the 25full advantage of the statistical characteristics of white noise to perturb the signal in its true solution neighborhood,and to cancel itself out after serving its purpose;therefore,it 27represents a substantial improvement over the original EMD and is a truly noise-assisted data analysis (NADA)method.29Keywords :1.Introduction 31Empirical Mode Decomposition (EMD)has been proposed recently 1,2as an adap-tive time–frequency data analysis method.It has proven to be quite versatile in 33a broad range of applications for extracting signals from data generated in noisy nonlinear and nonstationary processes (see,for example,Refs.3and 4).As useful 35as EMD proved to be,it still leaves some annoying diﬃculties unresolved.One of the major drawbacks of the original EMD is the frequent appearance 37of mode mixing,which is deﬁned as a single Intrinsic Mode Function (IMF)either consisting of signals of widely disparate scales,or a signal of a similar scale residing39in diﬀerent IMF components.Mode mixing is a consequence of signal intermittency.1July24,200813:6WSPC/244-AADA000042Z.Wu&N.E.HuangAs discussed by Huang et al.,1,2the intermittence could not only cause serious 1aliasing in the time–frequency distribution,but also make the physical meaningof individual IMF unclear.To alleviate this drawback,Huang et al.2proposed the 3intermittence test,which can indeed ameliorate some of the diﬃculties.However,the approach itself has its own problems:First,the intermittence test is based on 5a subjectively selected scale.With this subjective intervention,the EMD ceases tobe totally adaptive.Secondly,the subjective selection of scales works if there are 7clearly separable and deﬁnable timescales in the data.In case the scales are notclearly separable but mixed over a range continuously,as in the case of the majority 9of natural or man-made signals,the intermittence test algorithm with subjectivelydeﬁned timescales often does not work very well.11To overcome the scale separation problem without introducing a subjective intermittence test,a new noise-assisted data analysis(NADA)method is proposed, 13the Ensemble EMD(EEMD),which deﬁnes the true IMF components as the meanof an ensemble of trials,each consisting of the signal plus a white noise ofﬁnite 15amplitude.With this ensemble approach,we can clearly separate the scale nat-urally without any a priori subjective criterion selection.This new approach is 17based on the insight gleaned from recent studies of the statistical properties ofwhite noise,5,6which showed that the EMD is eﬀectively an adaptive dyadicﬁlter 19bank a when applied to white noise.More critically,the new approach is inspired bythe noise-added analyses initiated by Flandrin et al.7and Gledhill.8Their results 21demonstrated that noise could help data analysis in the EMD.The principle of the EEMD is simple:the added white noise would populate 23the whole time–frequency space uniformly with the constituting components ofdiﬀerent scales.When signal is added to this uniformly distributed white back-25ground,the bits of signal of diﬀerent scales are automatically projected onto properscales of reference established by the white noise in the background.Of course, 27each individual trial may produce very noisy results,for each of the noise-addeddecompositions consists of the signal and the added white noise.Since the noise in 29each trial is diﬀerent in separate trials,it is canceled out in the ensemble mean ofenough trials.The ensemble mean is treated as the true answer,for,in the end, 31the only persistent part is the signal as more and more trials are added in theensemble.33The critical concept advanced here is based on the following observations:1.A collection of white noise cancels each other out in a time-space ensemble mean;35therefore,only the signal can survive and persist in theﬁnal noise-added signalensemble mean.37a A dyadicﬁlter bank is a collection of band-passﬁlters that have a constant band-pass shape(e.g.a Gaussian distribution)but with neighboringﬁlters covering half or double of the frequencyrange of any singleﬁlter in the bank.The frequency ranges of theﬁlters can be overlapped.Forexample,a simple dyadicﬁlter bank can includeﬁlters covering frequency windows such as50to120Hz,100to240Hz,200to480Hz,etc.July24,200813:6WSPC/244-AADA00004Ensemble Empirical Mode Decomposition32.Finite,not inﬁnitesimal,amplitude white noise is necessary to force the ensemble1to exhaust all possible solutions;theﬁnite magnitude noise makes the diﬀerentscale signals reside in the corresponding IMF,dictated by the dyadicﬁlter banks, 3and render the resulting ensemble mean more meaningful.3.The true and physically meaningful answer to the EMD is not the one without5noise;it is designated to be the ensemble mean of a large number of trialsconsisting of the noise-added signal.7This EEMD proposed here has utilized all these important statistical character-istics of noise.We will show that the EEMD utilizes the scale separation principle 9of the EMD,and enables the EMD method to be a truly dyadicﬁlter bank forany data.By addingﬁnite noise,the EEMD eliminates mode mixing in all cases 11automatically.Therefore,the EEMD represents a major improvement of the EMDmethod.13In the following sections,a systematic exploration of the relation between noise and signal in data will be presented.Studies of Flandrin et al.5and Wu and Huang6 15have revealed that the EMD serves as a dyadicﬁlter for various types of noise.Thisimplies that a signal of a similar scale in a noisy data set could possibly be contained 17in one IMF component.It will be shown that adding noise withﬁnite rather thaninﬁnitesimal amplitude to data indeed creates such a noisy data set;therefore, 19the added noise,havingﬁlled all the scale space uniformly,can help to eliminatethe annoying mode mixing problemﬁrst noticed by Huang et al.2Based on these 21results,we will propose formally the concepts of NADA and noise-assisted signalextraction(NASE),and will develop a method called the EEMD,which is based 23on the original EMD method,to make NADA and NASE possible.The paper is arranged as follows.Section2will summarize previous attempts of 25using noise as a tool in data analysis.Section3will introduce the EEMD method,illustrate more details of the drawbacks associated with mode mixing,present con-27cepts of NADA and of NASE,and introduce the EEMD in detail.Section4willdisplay the usefulness and capability of the EEMD through examples.Section5 29will further discuss the related issues to the EEMD,its drawbacks,and their corre-sponding solutions.A summary and discussion will be presented in theﬁnal section 31of the main text.Two appendices will discuss some related issues of EMD algorithmand a Matlab EMD/EEMD software for research community to use.332.A Brief Survey of Noise Assisted Data AnalysisThe word“noise”can be traced etymologically back to its Latin root of“nausea,”35meaning“seasickness.”Only in Middle English and Old French does it start to gainthe meaning of“noisy strife and quarrel,”indicating something not at all desirable.37Today,the deﬁnition of noise varies in diﬀerent circumstances.In science and engi-neering,noise is deﬁned as disturbance,especially a random and persistent kind 39that obscures or reduces the clarity of a signal.In natural phenomena,noise couldJuly24,200813:6WSPC/244-AADA000044Z.Wu&N.E.Huangbe induced by the process itself,such as local and intermittent instabilities,irresolv-1able subgrid phenomena,or some concurrent processes in the environment in whichthe investigations are conducted.It could also be generated by the sensors and 3recording systems when observations are made.When eﬀorts are made to under-stand data,important diﬀerences must be considered between the clean signals that 5are the direct results of the underlying fundamental physical processes of our inter-est(“the truth”)and the noise induced by various other processes that somehow 7must be removed.In general,all data are amalgamations of signal and noise,i.e.x(t)=s(t)+n(t),(1) 9in which x(t)is the recorded data,and s(t)and n(t)are the true signal andnoise,respectively.Because noise is ubiquitous and represents a highly undesirable 11and dreaded part of any data,many data analysis methods were designed speciﬁ-cally to remove the noise and extract the true signals in data,although often not 13successful.Since separating the signal and the noise in data is necessary,three important 15issues should be addressed:(1)The dependence of the results on the analysis meth-ods used and assumptions made on the data.(For example,a linear regression of 17data implicitly assumes the underlying physics of the data to be linear,while aspectrum analysis of data implies the process is stationary.)(2)The noise level to 19be tolerated in the extracted“signals,”for no analysis method is perfect,and inalmost all cases the extracted“signals”still contain some noise.(3)The portion 21of real signal obliterated or deformed through the analysis processing as part ofthe noise.(For example,Fourierﬁltering can remove harmonics through low-pass 23ﬁltering and thus deform the waveform of the fundamentals.)All these problems cause misinterpretation of data,and the latter two issues are 25speciﬁcally related to the existence and removal of noise.As noise is ubiquitous,steps must be taken to insure that any meaningful result from the analysis should 27not be contaminated by noise.To avoid possible illusion,the null hypothesis testagainst noise is often used with the known noise characteristics associated with the 29analysis method.6,9,7Although most data analysis techniques are designed speciﬁ-cally to remove noise,there are,however,cases when noise is added in order to help 31data analysis,to assist the detection of weak signals,and to delineate the under-lying processes.The intention here is to provide a brief survey of the beneﬁcial 33utilization of noise in data analysis.The earliest known utilization of noise in aiding data analysis was due to Press 35and Tukey10known as pre-whitening,where white noise was added toﬂatten thenarrow spectral peaks in order to get a better spectral estimation.Since then, 37pre-whitening has become a very common technique in data analysis.For exam-ple,Fuenzalida and Rosenbluth11added noise to process climate data;Link and 39Buckley,12and Zala et al.13used noise to improve acoustic signal;Strickland andIl Hahn14used wavelet and added noise to detect objects in general;and Trucco15 41used noise to help design specialﬁlters for detecting embedded objects on the oceanJuly24,200813:6WSPC/244-AADA00004Ensemble Empirical Mode Decomposition5ﬂoor experimentally.Some general problems associated with this approach can be 1found in the works by Priestley,16Kao et al.,17Politis,18and Douglas et al.19 Another category of popular use of noise in data analysis is more related to the 3analysis method than to help extracting the signal from the data.Adding noiseto data helps to understand the sensitivity of an analysis method to noise and 5the robustness of the results obtained.This approach is used widely;for example,Cichocki and Amari20added noise to various data to test the robustness of the 7independent component analysis(ICA)algorithm,and De Lathauwer et al.21usednoise to identify error in ICA.9Adding noise to the input to speciﬁcally designed nonlinear detectors could also be beneﬁcial to detecting weak periodic or quasi-periodic signals based on a physical 11process called stochastic resonance.The study of stochastic resonance was pioneeredby Benzi and his colleagues in the early1980s.The details of the development of 13the theory of stochastic resonance and its applications can be found in a lengthyreview paper by Gammaitoni et al.22It should be noted here that most of the 15past applications(including those mentioned earlier)have not used the cancellationeﬀects associated with an ensemble of noise-added cases to improve their results.17Speciﬁc to analysis using EMD,Huang et al.23added inﬁnitesimal magnitude noise to earthquake data in an attempt to prevent the low frequency mode from 19expanding into the quiescent region.But they failed to realize fully the implicationsof the added noise in the EMD method.The true advances related to the EMD 21method had to wait until the two pioneering works by Gledhill8and Flandrin et al.7 Flandrin et al.7used added noise to overcome one of the diﬃculties of the 23original EMD method.As the EMD is solely based on the existence of extrema(either in amplitude or in curvature),the method ceases to work if the data lacks 25the necessary extrema.An extreme example is in the decomposition of a Diracpulse(delta function),where there is only one extrema in the whole data set.To 27overcome the diﬃculty,Flandrin et al.7suggested adding noise with inﬁnitesimalamplitude to the Dirac pulse so as to make the EMD algorithm operable.Since 29the decomposition results are sensitive to the added noise,Flandrin et al.7ran anensemble of5000decompositions,with diﬀerent versions of noise,all of inﬁnitesimal 31amplitude.Though they used the mean as theﬁnal decomposition of the Diracpulse,they deﬁned the true answer as33E{d[n]+εr k[n]},(2)d[n]=lime→0+in which,[n]represents n th data point,d[n]is the Dirac function,r k[n]is a random 35number,εis the inﬁnitesimal parameter,and E{}is the expected value.Flandrin’snovel use of the added noise has made the EMD algorithm operable for a data set 37that could not be previously analyzed.Another novel use of noise in data analysis is by Gledhill,8who used noise to 39test the robustness of the EMD algorithm.Although an ensemble of noise was used,he never used the cancellation principle to deﬁne the ensemble mean as the true 41answer.Based on his discovery(that noise could cause the EMD to produce slightlyJuly24,200813:6WSPC/244-AADA000046Z.Wu&N.E.Huangdiﬀerent outcomes),he assumed that the result from the clean data without noise 1was the true answer and thus designated it as the reference.He then deﬁned thediscrepancy,∆,as3∆=mj=1t(cr j(t)−cn j(t))21/2,(3)where cr j and cn j are the j th component of the IMF without and with noise added, 5and m is the total number of IMFs generated from the data.In his extensive study of the detailed distribution of the noise-caused“discrepancy,”he concluded that 7the EMD algorithm is reasonably stable for small perturbations.This conclusion is in slight conﬂict with his observations that the perturbed answer with inﬁnitesimal 9noise showed a bimodal distribution of the discrepancy.Gledhill had also pushed the noise-added analysis in another direction:He had 11proposed to use an ensemble mean of noise-added analysis to form a“Composite Hilbert spectrum.”As the spectrum is non-negative,the added noise could not 13cancel out.He then proposed to keep a noise-only spectrum and subtract it from the full noise-added spectrum at the end.This non-cancellation of noise in the 15spectrum,however,forced Gledhill8to limit the noise used to be of small magnitude, so that he could be sure that there would not be too much interaction between the 17noise-added and the original clean signal,and that the contribution of the noise to theﬁnal energy density in the spectrum would be negligible.19Although noise of inﬁnitesimal amplitude used by Gledhill8has improved the conﬁdence limit of theﬁnal spectrum,Gledhill explored neither fully the cancella-21tion property of the noise nor the power ofﬁnite perturbation to explore all possible solutions.Furthermore,it is well known that whenever there is intermittence,the 23signal without noise can produce IMFs with mode mixing.There is no justiﬁcation to assume that the result without added noise is the truth or the reference sig-25nal.These reservations notwithstanding,all these studies by Flandrin et al.7and Gledhill8had still greatly advanced the understanding of the eﬀects of noise in the 27EMD method,though the crucial eﬀects of noise had yet to be clearly articulated and fully explored.29In the following,the new noise-added EMD approach will be explained,in which the cancellation principle will be fully utilized,even withﬁnite amplitude noise.Also 31emphasized is theﬁnding that the true solution of the EMD method should be the ensemble mean rather than the clean data.This full presentation of the new method 33will be the subject of the next section.3.Ensemble Empirical Mode Decomposition353.1.The empirical mode decompositionThis section starts with a brief review of the original EMD method.The detailed 37method can be found in the works of Huang et al.1and Huang et al.2Diﬀerent to almost all previous methods of data analysis,the EMD method is adaptive,with 39July24,200813:6WSPC/244-AADA00004Ensemble Empirical Mode Decomposition7 the basis of the decomposition based on and derived from the data.In the EMD 1approach,the data X(t)is decomposed in terms of IMFs,c j,i.e.x(t)=nj=1c j+r n,(4)3where r n is the residue of data x(t),after n number of IMFs are extracted.IMFs are simple oscillatory functions with varying amplitude and frequency,and hence 5have the following properties:1.Throughout the whole length of a single IMF,the number of extrema and the 7number of zero-crossings must either be equal or diﬀer at most by one(althoughthese numbers could diﬀer signiﬁcantly for the original data set);92.At any data location,the mean value of the envelope deﬁned by the local maximaand the envelope deﬁned by the local minima is zero.11In practice,the EMD is implemented through a sifting process that uses only local extrema.From any data r j−1,say,the procedure is as follows:(1)identify all 13the local extrema(the combination of both maxima and minima)and connect all these local maxima(minima)with a cubic spline as the upper(lower)envelope; 15(2)obtain theﬁrst component h by taking the diﬀerence between the data and thelocal mean of the two envelopes;and(3)Treat h as the data and repeat steps1and 172as many times as is required until the envelopes are symmetric with respect to zero mean under certain criteria.Theﬁnal h is designated as c j.A complete sifting 19process stops when the residue,r n,becomes a monotonic function from which no more IMFs can be extracted.21Based on this simple description of EMD,Flandrin et al.5and Wu and Huang6 have shown that,if the data consisted of white noise which has scales populated 23uniformly through the whole timescale or time–frequency space,the EMD behaves as a dyadicﬁlter bank:the Fourier spectra of various IMFs collapse to a single 25shape along the axis of logarithm of period or frequency.Then the total number of IMFs of a data set is close to log2N with N the number of total data points. 27When the data is not pure noise,some scales could be missing;therefore,the total number of the IMFs might be fewer than log2N.Additionally,the intermittency 29of signals in certain scale would also cause mode mixing.3.2.Mode mixing problem31“Mode mixing”is deﬁned as any IMF consisting of oscillations of dramatically dis-parate scales,mostly caused by intermittency of the driving mechanisms.When 33mode mixing occurs,an IMF can cease to have physical meaning by itself,suggest-ing falsely that there may be diﬀerent physical processes represented in a mode. 35Even though theﬁnal time–frequency projection could rectify the mixed mode to some degree,the alias at each transition from one scale to another would irrecov-37erably damage the clean separation of scales.Such a drawback wasﬁrst illustratedJuly24,200813:6WSPC/244-AADA000048Z.Wu&N.E.Huangby Huang et al.2in which the modeled data was a mixture of intermittent high-1frequency oscillations riding on a continuous low-frequency sinusoidal signal.Analmost identical example used by Huang et al.2is presented here in detail as an 3illustration.The data and its sifting process are illustrated in Fig.1.The data has its funda-5mental part as a low-frequency sinusoidal wave with unit amplitude.At the threemiddle crests of the low-frequency wave,high-frequency intermittent oscillations 7with an amplitude of0.1are riding on the fundamental,as panel(a)of Fig.1shows.The sifting process starts with identifying the maxima(minima)in the 9data.In this case,15local maxima are identiﬁed,with theﬁrst and the last comingfrom the fundamental,and the other13caused mainly by intermittent oscillations 11(panel(b)).As a result,the upper envelope resembles neither the upper envelope ofthe fundamental(which is aﬂat line at one)nor the upper one of the intermittent 13oscillations(which is supposed to be the fundamental outside intermittent areas).Rather,the envelope is a mixture of the envelopes of the fundamental and of the 15(a)(b)(c)(d)Fig.1.The veryﬁrst step of the sifting process.Panel(a)is the input;panel(b)identiﬁes localmaxima(gray dots);panel(c)plots the upper envelope(upper gray dashed line)and low envelope(lower gray dashed line)and their mean(bold gray line);and panel(d)is the diﬀerence betweenthe input and the mean of the envelopes.July24,200813:6WSPC/244-AADA00004Ensemble Empirical Mode Decomposition9Fig.2.The intrinsic mode functions of the input displayed in Fig.1(a).intermittent signals that lead to a severely distorted envelope mean(the thick grey 1line in panel(c)).Consequently,the initial guess of theﬁrst IMF(panel(d))is themixture of both the low frequency fundamental and the high-frequency intermittent 3waves,as shown in Fig.2.An annoying implication of such scale mixing is related to unstableness and lack 5of the uniqueness of decomposition using the EMD.With stoppage criterion givenand end-point approach prescribed in the EMD,the application of the EMD to 7any real data results in a unique set of IMFs,just as when the data is processedby other data decomposition methods.This uniqueness is here referred to as“the 9mathematical uniqueness,”and satisfaction to the mathematical uniqueness is theminimal requirement for any decomposition method.The issue that is emphasized 11here is what we refer to as“the physical uniqueness.”Since real data almost alwayscontains a certain amount of random noise or intermittences that are not known 13to us,an important issue,therefore,is whether the decomposition is sensitive tonoise.If the decomposition is insensitive to added noise of small butﬁnite ampli-15tude and bears little quantitative and no qualitative change,the decomposition isgenerally considered stable and satisﬁes the physical uniqueness;and otherwise, 17the decomposition is unstable and does not satisfy the physical uniqueness.Theresult from decomposition that does not satisfy the physical uniqueness may not be 19reliable and may not be suitable for physical interpretation.For many traditionaldata decomposition methods with prescribed base functions,the uniqueness of the 21July24,200813:6WSPC/244-AADA0000410Z.Wu&N.E.Huangsecond kind is automatically satisﬁed.Unfortunately,the EMD in general does not 1satisfy this requirement due to the fact that decomposition is solely based on thedistribution of extrema.3To alleviate this drawback,Huang et al.2proposed an intermittence test that subjectively extracts the oscillations with periods signiﬁcantly smaller than a pre-5selected value during the sifting process.The method works quite well for thisexample.However,for complicated data with scales variable and continuously dis-7tributed,no single criterion of intermittence test can be selected.Furthermore,themost troublesome aspect of this subjectively pre-selected criterion is that it lacks 9physical justiﬁcations and renders the EMD nonadaptive.Additionally,mode mix-ing is also the main reason that renders the EMD algorithm unstable:Any small 11perturbation may result in a new set of IMFs as reported by Gledhill.8Obviously,the intermittence prevents EMD from extracting any signal with similar scales.13To solve these problems,the EEMD is proposed,which will be described in thefollowing sections.153.3.Ensemble empirical mode decompositionAs given in Eq.(1),all data are amalgamations of signal and noise.To improve the 17accuracy of measurements,the ensemble mean is a powerful approach,where dataare collected by separate observations,each of which contains diﬀerent noise.To 19generalize this ensemble idea,noise is introduced to the single data set,x(t),as ifseparate observations were indeed being made as an analog to a physical experiment 21that could be repeated many times.The added white noise is treated as the possiblerandom noise that would be encountered in the measurement process.Under such 23conditions,the i th“artiﬁcial”observation will bex i(t)=x(t)+w i(t).(5) 25In the case of only one observation,one of the multiple-observation ensembles is mimicked by adding not arbitrary but diﬀerent copies of white noise,w i(t),to 27that single observation as given in Eq.(5).Although adding noise may result insmaller signal-to-noise ratio,the added white noise will provide a uniform reference 29scale distribution to facilitate EMD;therefore,the low signal–noise ratio does notaﬀect the decomposition method but actually enhances it to avoid the mode mixing.31Based on this argument,an additional step is taken by arguing that adding whitenoise may help to extract the true signals in the data,a method that is termed 33EEMD,a truly NADA method.Before looking at the details of the new EEMD,a review of a few properties of 35the original EMD is presented:(1)the EMD is an adaptive data analysis method that is based on local charac-37teristics of the data,and hence,it catches nonlinear,nonstationary oscillationsmore eﬀectively;39。

Posterior probability intervals for wavelet thresholding

Posterior probability intervals for wavelet thresholdingStuart Barber,Guy P.Nason,and Bernard W.SilvermanUniversity of Bristol,UK.AbstractWe use cumulants to derive Bayesian credible intervals for wavelet regression estimates.The ﬁrst four cumulants of the posterior distribution of the estimates are expressed in terms of theobserved data and integer powers of the mother wavelet functions.These powers are closelyapproximated by linear combinations of wavelet scaling functions at an appropriateﬁner scale.Hence,a suitable modiﬁcation of the discrete wavelet transform allows the posterior cumulantsto be found efﬁciently for any given data set.Johnson transformations then yield the credibleintervals themselves.Simulations show that these intervals have good coverage rates,evenwhen the underlying function is inhomogeneous,where standard methods fail.In the casewhere the curve is smooth,the performance of our intervals remains competitive with establishednonparametric regression methods.Keywords:Bayes estimation;Cumulants;Curve estimation;Interval estimates;Johnson curves;Nonparametric regression;Powers of wavelets.1IntroductionConsider the estimation of a function from an observed data vector satisfyingwhere and the are independently distributed.There are many methods of estimating smooth functions,such as spline smoothing(Green and Silverman,1994),kernel estimation(Wand and Jones,1995),and local polynomial regression(Fan and Gijbels,1996).In most cases,such point estimates can be supplemented by interval estimates with some speciﬁed nominal coverage probability or signiﬁcance level.A recent proposal for estimation of inhomogeneous is wavelet thresholding(Donoho and Johnstone1994,1995).The representation of in terms of a wavelet basis is typically sparse, concentrating most of the signal in the data into a few large coefﬁcients,whilst the noise is spread “evenly”across the coefﬁcients due to the orthonormality of the wavelet basis.The data is denoised by a thresholding rule of some sort to discard“small”coefﬁcients and retain,possibly with some modiﬁcation,those coefﬁcients which are thought to contain the signal.Several authors have described Bayesian wavelet thresholding rules,placing prior distributions on the wavelet coefﬁcients.We consider a means of approximating the posterior distribution of each ,using the same prior as the BayesThresh method of Abramovich,Sapatinas and Silverman (1998).Posterior probability intervals of any nominal coverage probability can then be calculated. Our approach can also be applied to other Bayesian wavelet thresholding rules,such as those surveyed by Chipman and Wolfson(1999),Abramovich and Sapatinas(1999),and Vidakovic(1998).We brieﬂy review the wavelet thresholding approach to curve estimation in section2,including two Bayesian methods of wavelet thresholding.In section3,we derive our WaveBand method of estimating the posterior distribution of given the observed data.We present an example and simulation results in section4and make some concluding remarks in section5.2Wavelets and wavelet thresholding2.1WaveletsWavelets provide a variety of orthonormal bases of,the space of square integrable functions on;each basis is generated from a scaling function,denoted,and an associated wavelet,. The wavelet basis consists of dilations and translations of these functions.For,the wavelet at level and location is given by(1) with an analogous deﬁnition for.The scaling function is sometimes referred to as the father wavelet,but we avoid this terminology.A function can be represented as(2)with and.Daubechies(1992)derived two families of wavelet bases which give sparse representations of wide sets of functions.(Technically,by choosing a wavelet with suitable properties,we can generate an unconditional wavelet basis in a wide set of function spaces;for further details, see Abramovich et al.(1998).)Generally,smooth portions of are represented by a small number of coarse scale(low level)coefﬁcients,while local inhomogeneous features such as high frequency events,cusps and discontinuities are represented by coefﬁcients atﬁner scales(higher levels).For our nonparametric regression problem,we have discrete data and hence consider the discrete wavelet transform(DWT).Given a vector,where,the DWT of is ,where is an orthonormal matrix and is a vector of the discrete scaling coefﬁcient and discrete wavelet coefﬁcients.These are analogous to the coefﬁcients in(2),with.Our data are restricted to lie in,requiring boundary conditions;we assume that is periodic at the boundaries.Other boundary conditions include the assumption that is reﬂected at the boundaries,or the“wavelets on the interval”transform of Cohen,Daubechies and Vial(1993)can be used.The pyramid algorithm of Mallat(1989)computes in operations,provided. The algorithm iteratively computes the and from the.From the vector,the inverse DWT(IDWT)can be used to reconstruct the original data.The IDWT starts with the overall scaling and wavelet coefﬁcients and and reconstructs the;it then proceeds iteratively toﬁner levels,reconstructing the from the and.22.2Curve estimation by wavelet thresholdingSince the DWT is an orthonormal transformation,white noise in the data domain is transformed towhite noise in the wavelet domain.If is the DWT of,and thevector of empirical coefﬁcients obtained by applying the DWT to the data,then,where is a vector of independent variates.Wavelet thresholding assumes implicitly that“large”and“small”represent signal and noise respectively.Various thresholding ruleshave been proposed to determine which coefﬁcients are“large”and“small”;see Vidakovic(1999)or Abramovich,Bailey and Sapatinas(2000)for reviews.The true coefﬁcients are estimated byapplying the thresholding rule to the empirical coefﬁcients to obtain estimates,and the sampled function values are estimated by applying the IDWT to obtain where denotes the transpose of;symbolically,we can represent this IDWT as the sum(3)Conﬁdence intervals for the resulting curve estimates have received some attention in the wavelet literature.Brillinger(1994)derived an estimate of var when the wavelet decomposition involved Haar wavelets,and Brillinger(1996)showed that is asymptotically normal under certain conditions. Bruce and Gao(1996)extended the estimation of var to the case of non-Haar wavelets,and gave approximate conﬁdence intervals using the asymptotic normality of.Chipman, Kolaczyk and McCulloch(1997)presented approximate credible intervals for their adaptive Bayesian wavelet thresholding method,which we discuss in section2.3.2,while Picard and Tribouley(2000) derive bias corrected conﬁdence intervals for wavelet thresholding estimators.2.3Bayesian wavelet regression2.3.1IntroductionSeveral authors have proposed Bayesian wavelet regression estimates,involving priors on the wavelet coefﬁcients,which are updated by the observed coefﬁcients to obtain posterior distributions .Point estimates can be computed from these posterior distributions and the IDWT employed to estimate in the usual fashion outlined above.Some proposals have included priors on ;we restrict ourselves to the situation where can be well estimated from the data.The majority of Bayesian wavelet shrinkage rules have employed mixture distributions as priors on the coefﬁcients,to model the notion that a small proportion of coefﬁcients contain substantial signal.Chipman et al.(1997)and Crouse,Nowak and Baraniuk(1998)considered mixtures of two normal distributions,while Abramovich et al.(1998),Clyde,Parmigiani and Vidakovic(1998)and Clyde and George(2000)used mixtures of a normal and a point mass.Other proposals include a mixture of a point mass and a-distribution used by Vidakovic(1998),and an inﬁnite mixture of normals considered by Holmes and Denison(1999).More thorough reviews are given by Chipman and Wolfson(1999)and Abramovich and Sapatinas(1999).32.3.2Adaptive Bayesian wavelet shrinkageThe ABWS method of Chipman et al.(1997)places an independent prior on each:(4) where Bernoulli;hyperparameters,and are determined from the data by empirical Bayes methods.At level,the proportion of non-zero coefﬁcients is represented by,while and represent the magnitude of negligible and non-negligible coefﬁcients respectively.Given,the empirical coefﬁcients are independently,so the posterior distribution is a mixture of two normal components independently for each. Chipman et al.(1997)use the mean of this mixture as their estimator,and similarly use the variance of to approximate the variance of their ABWS estimate of.Estimating each coefﬁcient by the mean of its posterior distribution is the Bayes rule under the loss function.They plot uncertainty bands of sd.These bands are useful in representing the uncertainty in the estimate,but are based on an assumption of normality despite being a sum of random variables with mixture distributions.2.3.3BayesThreshThe BayesThresh method of Abramovich et al.(1998)also places independent priors on the coefﬁcients:(5) where and is a probability mass at zero.This is a limiting case of the ABWS prior(4).The hyperparameters are assumed to be of the form and min for non-negative constants and chosen empirically from the data and and selected by the user. Abramovich et al.(1998)show that choices of and correspond to choosing priors within certain Besov spaces,incorporating prior knowledge about the smoothness of in the prior.Chipman and Wolfson(1999)also discuss the interpretation of and.In the absence of any such prior knowledge, Abramovich et al.(1998)show that the default choice,is robust to varying degrees of smoothness of.The prior speciﬁcation is completed by placing a non-informative prior on the scaling coefﬁcient,which thus has the posterior distribution,and is estimated by.The resulting posterior distribution of given the observed value of is again independent for each and is given by(6) where,withand.The BayesThresh approach minimises the loss in the wavelet domain by using the posterior median of as the point estimate;Abramovich et al.(1998)show4that this gives a level-dependent true thresholding rule.The BayesThresh method is implemented in the WaveThresh package for SPlus(Nason,1998).3WaveBand3.1Posterior cumulants of the regression curveWe now consider the posterior density of for each.From(3),we see that is the convolution of the posteriors of the wavelet coefﬁcients and the scaling coefﬁcient,(7)this is a complicated mixture,and is impractical to evaluate analytically.Direct simulation from the posterior is extremely time consuming.Instead we estimate theﬁrst four cumulants of(7)andﬁt a distribution which matches these values.Evaluating cumulants of requires the use of powers of wavelets for,and,which we discuss in section3.2.We thenﬁt a parametric distribution to in section3.3.If the moment generating function of a random variable is written,then the cumulant generating function is.We write for the th cumulant of,given by the th derivative of,evaluated at.Note that theﬁrst moments uniquely determine theﬁrst cumulants and vice-versa.Further details of cumulants and their properties and uses can be found in Barndorff-Nielsen and Cox(1989)or Stuart and Ord(1994,chapter3).Theﬁrst four cumulants each have a direct interpretation;and are the mean and variance of respectively,while is the skewness and is the kurtosis.If is normally distributed then both and are zero.We make use of two standard properties of cumulants.If and are independent random variables and and are real constants,then(8)and(9) Applying(8)and(9)to(7),we can see that the cumulants of are given by(10)Once the cumulants of the wavelet coefﬁcients are known,this sum can be evaluated directly using the IDWT when,but for,and,the computation involves powers of wavelets.The posterior distributions(6)for the wavelet coefﬁcients using BayesThresh are of the form ,where,,and is a point mass at zero.Then5so the moments of(6)are easily obtained.From these,we can derive the cumulants of:Since the scaling coefﬁcient has a normal posterior distribution,theﬁrst two cumulants are and;all higher order cumulants are zero.3.2Powers of waveletsThe parallel between(10)and the sum(3)evaluated by the IDWT is clear,and we shall describe a means of taking advantage of the efﬁcient IDWT algorithm to evaluate(10).For Haar wavelets, this is trivial;the Haar scaling function and mother wavelet are and,where is the indicator function,hence and.Moreover,,,and ,all terms which can be included in a modiﬁed version of the IDWT algorithm which incorporates scaling function coefﬁcients.Since representing by scaling functions and wavelets works in the Haar case,we consider a similar approach for other wavelet bases.Following Herrick(2000,pp.69),we approximate a general wavelet,,by(11)for,where is a positive integer;the choice of is discussed below.We use scaling functions rather than wavelets as the span of the set of scaling functions at a given level is the same as that of the union of and wavelets at levels.Moreover,if scaling functionsare used to approximate some function,and both and have at least derivatives,then the mean squared error in the approximation is bounded by,where is some positive constant; see,for example,Vidakovic(1999,p.87).To approximate for someﬁxed,weﬁrst compute using the cascade algorithm (Daubechies,1992,pp.205),then take the DWT of and set the coefﬁcients to be equal to the scaling function coefﬁcients at level,where.Recall that the wavelets at level are simply shifts of each other;from(1),hence(12) As we are assuming periodic boundary conditions,the can be cycled periodically.6(a)0.00.20.40.60.8 1.0-0.100.00.1••••••••••(b)24680.00.20.40.60.8••••••••••(c)24680.00.20.40.60.81.0••••••••••(d)24680.00.20.40.60.8Approximation levelApproximation level Approximation levelM S E r a t i oM S E r a t i oM S E r a t i oFigure 1:Daubechies’extremal phase wavelet with two vanishing moments (panel a)and accuracy of estimating for by scaling functions at level .The mean square errors of the estimates,divided by the norm of ,are plotted against :panels (b),(c),and (d)show results for ,and respectively.The vertical lines are at level 3,the level at which exists.Owing to the localised nature of wavelets,the coefﬁcientsused to approximatecan be found by inserting zeros into the vector of:Approximation (11)cannot be used for wavelets at the ﬁnest levels .Werepresent these wavelets by both scaling functions and wavelets at the ﬁnest level of detail,level,using the block-shifting technique outlined above to make the computations more efﬁcient.In all the cases we have examined,has been sufﬁcient for a highly accurate approximation;examples are shown in ﬁgures 1and 2.Consider approximating the powers of Daubechies’extremal phase wavelet with two vanishing moments;this wavelet is extremely non-smooth and so can be regarded as a near worst-case scenario for the approximation.Panel (a)of ﬁgure 1shows ,while panels (b)-(d)show the mean square error in our approximation divided by the norm of the function being approximated,for respectively.In each plot (b)-(d),the vertical line is at resolution level ,the level at which thewavelet whose power is being estimated exists.The approximation is excellent forin each case,with little improvement at level .70.00.20.40.60.8 1.00.00.040.080.00.20.40.60.8 1.00.00.040.080.120.00.20.40.60.8 1.00.00.040.080.00.20.40.60.8 1.0-0.03-0.02-0.010.00.010.00.20.40.60.8 1.0-0.03-0.02-0.010.00.010.00.20.40.60.8 1.0-0.03-0.02-0.010.00.010.00.20.40.60.8 1.00.0020.0060.0100.00.20.40.60.8 1.00.00.0040.0080.0120.00.20.40.60.8 1.00.0020.0060.010Figure 2:Approximations to powers of Daubechies’least asymmetric wavelet with eight vanishing moments;the powers are indicated at the top of each column.Solid lines are wavelet powers and dotted lines show approximations using scaling functions at level .From top to bottom,graphs show approximation at levels ,,and ;the original wavelet is at level .Figure 2shows approximations to powers of Daubechies’least asymmetric wavelet with eight vanishing moments as the approximation level increases.Again,the base wavelet is at level,and approximations are shown for (top row),,and(bottom row).In each case,the solid line is the wavelet power and the dotted line is the ing (12),we can now re-write (10)asfor suitable coefﬁcients ,and use a modiﬁed version of the IDWT algorithm which incorporates scaling function coefﬁcients to evaluate this sum.83.3Posterior distribution of the regression curveWe must now estimate from its cumulants.Edgeworth expansions give poor results in the tails of the distribution,where we require a good approximation.Saddlepoint expansions improve on this, but require the cumulant generating function,while we only have theﬁrst four cumulants. Therefore,we approximate by a suitable parametric distribution.A family of distributions is the set of transformations of the normal curve described by Johnson (1949).As well as the normal distribution,Johnson curves fall into three categories;(a)the lognormal,,with,(b)the unbounded,,and(c)the bounded,,with,to which Hill,Hill and Holder(1976)added a limiting case of curves whereand shown inﬁgure3(solid line).Figure3also shows data formed by adding independent normally distributed noise to.The noise has mean zero and root signal to noise ratio(rsnr)3;the rsnr is deﬁned to be the ratio of the standard deviation of the data points to the standard deviation of the noise,.Dotted lines inﬁgure3mark upper and lower endpoints of99%credible intervals for for each calculated using our WaveBand method,using default parameters of,,and Daubechies’least asymmetric wavelet with eight vanishing moments.In this example,the credible intervals include the true value of in490of512cases,an empirical coverage rate of95.7%. The brief spikes which occur in the bands are typical of wavelet regression methods;they can be smoothed out by using different and,but this risks oversmoothing the data.9...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................0.00.20.40.60.8 1.00123Figure 3:Pointwise 99%WaveBand interval estimates (dotted line)for the piecewise polynomial signal (solid line).Dots indicate data on equally spaced points with the addition of independent normally distributed noise with mean zero and rsnr 3.Figure 4shows the mean,variance,skewness,and kurtosis of for each point .The mean is itself an estimate of and the variance is generally low except near the discontinuity at.We use the usual deﬁnitions of skewness and kurtosis,range from approximately -7.9to 7.5,and from approximately 1.7to almost 120,indicating that for some ,the posterior distribution has heavy tails.(For comparison the distribution has skewness 7.1and kurtosis 79.)The prior (5)has kurtosis ;note that in our example the largest values of kurtosis occur when the function is smooth;in these cases the majority of the wavelet coefﬁcients are zero,and hence is small.4.2Simulation results4.2.1Inhomogeneous signalsWe investigated the performance of our WaveBand credible intervals by simulation on the piecewise polynomial example of Nason and Silverman (1994)(denoted “PPoly”)and the standard “Blocks”,“Bumps”,“Doppler”and “HeaviSine”test functions of Donoho and Johnstone (1994),shown in ﬁgure 5.For each test function,100simulated data sets of length were created with rsnr100.00.20.40.60.8 1.01230.00.20.40.60.8 1.00.00.040.080.120.00.20.40.60.8 1.0-550.00.20.40.60.8 1.0020*********M e a nV a r i a n c eS k e w n e s sK u r t o s i sFigure 4:Mean,variance,skewness and kurtosis for the piecewise polynomial data shown in ﬁgure 3.4and the WaveBand and ABWS credible intervals evaluated at each data point for nominal coverage probabilities 0.90,0.95,and 0.99.The default hyperparameters and were used for WaveBand and both methods used Daubechies’least asymmetric wavelet with eight vanishing moments.Table 1shows the coverage rates and interval widths averaged over all points and the 100replications,with standard error shown in brackets.The WaveBand intervals have higher empirical coverage rates in each case,although still below the nominal coverage probabilities.Average widths of the WaveBand credible intervals are always greater than those of the ABWS intervals;one reason is that the ABWS method typically has a lower estimated variance.Moreover,the WaveBand posterior of is typically heavier-tailed than the normal distribution,as we saw in the piecewise polynomial example.The performance of the WaveBand intervals improves as the nominal coverage rate increases.In part,this can be attributed to the kurtosis of the posterior distributions.As the nominal coverage rates increase,the limits of the credible intervals move out into the tails of the posterior distributions.With heavy-tailed distributions,a small increase in the nominal coverage rate can produce a substantially wider interval.Figure 6examines the empirical coverage rates of the nominal 99%credible intervals in more detail.Solid lines denote the empirical coverage rates of the WaveBand intervals for each ,and dotted lines give the equivalent results for the ABWS intervals.Coverage varies greatly across each signal;unsurprisingly,the coverage is much better where the signal is smoother and less variable.This can be seen most clearly in the results for the piecewise polynomial and HeaviSine test functions,110.00.20.40.60.8 1.001230.00.20.40.60.8 1.0-20240.00.20.40.60.8 1.00123450.00.20.40.60.8 1.0-0.40.00.40.00.20.40.60.8 1.0-6-4-2024P p o l yB l o c k sB u m p sH e a v i S i n eD o p p l e rFigure 5:The piecewise polynomial of Nason and Silverman (1994)and the test functions of Donoho and Johnstone (1994).12Simulation results comparing mean coverage rates(CR)and interval widths for ABWS and WaveBand(denoted WB)credible intervals on the piecewise polynomial,Blocks,Bumps,Doppler, and HeaviSine test functions.Each test function was evaluated on points,the rsnr was 4,and100replications were done in each case.Standard errors are given in brackets.All methods were employed with Daubechies’least asymmetric wavelet with8vanishing moments,and the default hyperparameters and were used for WaveBand.130.00.20.40.60.81.00.00.40.80.00.20.40.60.81.00.00.40.80.00.20.40.60.8 1.00.00.40.80.00.20.40.60.81.00.00.40.80.00.20.40.60.8 1.00.00.40.8C o v e r a g eC o v e r a g eC o v e r a g eC o v e r a g eC o v e r a g eFigure 6:Empirical coverage rates of nominal 99%interval estimates for the indicated test functions evalauted at equally spaced data points.In each case,100simulated data sets with a rsnr of 4were used.Solid and dotted lines indicate coverage rates for the WaveBand method and ABWS methods respectively.14with sharp drops in performance near the discontinuities,and in the excellent coverage in the lower-frequency portion of the Doppler signal and the long constant parts of the Bumps signal.4.2.2Smooth signalsThe major advantage of wavelet thresholding as a nonparametric regression technique is the ability to model inhomogeneous signals such as those considered in section4.2.1.However,wavelet thresholding can also be used successfully on smooth signals,and we now consider such an example, the function.Table2shows the performance of ABWS and WaveBand credible intervals and conﬁdence intervals using smoothing splines for.The smoothing spline estimate of can be written spline,where is an matrix,so var spline.Hence we can construct an approximate conﬁdence interval for as spline where,and consider the random variable,, where is a double exponential variate with density function.Given an observation of,the15RSNR =20.95CR Width CR Width 0.939(.008)0.300(.002)0.990(.003)0.471(.004)WB 00.600Nominal coverage probability0.900.99CR WidthWB0.850(.010)0.143(.002)0.981(.002)0.276(.002)Spline0.934(.008)0.159(.002)0.493(.016)0.078(.003)0.643(.017)0.122(.004)Table 2:Simulation results comparing the mean coverage rate (CR)and interval widths forWaveBand ,smoothing spline,and ABWS methods on the functionposterior probability that is,where is the density function of a standard normal random variable,not a scaling function,and denotes convolution.Write for the distribution function associated with,and let and;then isAcknowledgmentsThe authors are grateful for the support of the EPSRC(grant GR/M10229)and by Unilever Research; GPN was also supported by EPSRC Advanced Research Fellowship AF/001664.The authors wish to thank Eric Kolaczyk and Thomas Yee for programs that implement the ABWS and spline methods respectively.The authors are also grateful for the constructive comments of the Joint Editor and two referees.ReferencesAbramovich, F.,Bailey,T.C.and Sapatinas,T.(2000).Wavelet analysis and its statistical applications.The Statistician49,1–29.Abramovich,F.and Sapatinas,T.(1999).Bayesian approach to wavelet decomposition and shrinkage.In M¨u ller,P.and Vidakovic,B.,editors,Bayesian Inference in Wavelet Based Models,volume141 of Lecture Notes in Statistics,pages33–50.Springer-Verlag,New York.Abramovich,F.,Sapatinas,T.and Silverman,B.W.(1998).Wavelet thresholding via a Bayesian approach.J.R.Statist.Soc.B60,725–749.Barndorff-Nielsen,O.E.and Cox,D.R.(1989).Asymptotic Techniques for Use in Statistics.Chapman and Hall,London.Brillinger,D.R.(1994).Some river wavelets.Environmetrics5,211–220.Brillinger,D.R.(1996).Uses of cumulants in wavelet analysis.J.Nonparam.Statist.6,93–114. Bruce,A.G.and Gao,H.Y.(1996).Understanding WaveShrink:variance and bias estimation.Biometrika83,727–745.Chipman,H.,Kolaczyk,E.and McCulloch,R.(1997).Adaptive Bayesian wavelet shrinkage.J.Am.Statist.Ass.92,1413–1421.Chipman,H.A.and Wolfson,L.J.(1999).Prior elicitation in the wavelet domain.In M¨u ller,P.and Vidakovic,B.,editors,Bayesian Inference in Wavelet Based Models,volume141of Lecture Notes in Statistics.Springer-Verlag,New York.Clyde,M.and George,E.I.(2000).Flexible empirical Bayes estimation for wavelets.J.R.Statist.Soc.B62,681–698.Clyde,M.,Parmigiani,G.and Vidakovic,B.(1998).Multiple shrinkage and subset selection in wavelets.Biometrika85,391–402.Cohen,A.,Daubechies,I.and Vial,P.(1993).Wavelets on the interval and fast wavelet transforms.p.Harm.Analysis1,54–81.Crouse,M.,Nowak,R.and Baraniuk,R.(1998).Wavelet-based statistical signal processing using hidden Markov models.IEEE Trans.Signal Processing46,886–902.Daubechies,I.(1992).Ten Lectures on Wavelets.SIAM,Philadelphia.Donoho,D.L.and Johnstone,I.M.(1994).Ideal spatial adaptation by wavelet shrinkage.Biometrika 81,425–455.Donoho,D.L.and Johnstone,I.M.(1995).Adapting to unknown smoothness via wavelet shrinkage.J.Am.Statist.Ass.90,1200–1224.18。

FREQUENCYCONTROL

Effects of frequency on motor load
• Motor load
• An approximate rule of thumb is that the connected motor load magnitude decreases by 2% if the frequency decreases by 1%.
• REG DOWN RESERVE
• Generation resources that decrease generation • Controllable load resources that increase load
• Responsive Reserve (RRS)
• Arrest frequency decay within the first few seconds of a significant frequency deviation on the ERCOT Transmission Grid using Primary Frequency Response and interruptible Load;
• Non Motor load
• It is a reasonably accurate statement to say that non-motor load magnitude does not vary as frequency is varied.
•Composite Load/Frequency Effect
Frequency control
ERCOT SCADA AGC
Load Frequency control
SecurityConstrained Economic Dispatch (SCED)

The Spectrum of the Partially Locked State for the Kuramoto Model

a r X i v :n l i n /0702043v 1 [n l i n .P S ] 22 F eb 2007The Spectrum of the Partially Locked State for the Kuramoto ModelRenato Mirollo*and Steven H.Strogatz †Dedicated to the memory of John David CrawfordAbstract We solve a longstanding stability problem for the Kuramoto model of coupled oscilla-tors.This system has attracted mathematical attention,in part because of its applications in ﬁelds ranging from neuroscience to condensed-matter physics,and also because it pro-vides a beautiful connection between nonlinear dynamics and statistical mechanics.The model consists of a large population of phase oscillators with all-to-all sinusoidal coupling.The oscillators’intrinsic frequencies are randomly distributed across the population ac-cording to a prescribed probability density,here taken to be unimodal and symmetric about its mean.As the coupling between the oscillators is increased,the system sponta-neously synchronizes:the oscillators near the center of the frequency distribution lock their phases together and run at the same frequency,while those in the tails remain unlocked and drift at diﬀerent frequencies.Although this “partially locked”state has been observed in simulations for decades,its stability has never been analyzed mathematically.Part of the diﬃculty is in formulating a reasonable inﬁnite-N limit of the model.Here we describe such a continuum limit,and prove that the corresponding partially locked state is,in fact,neutrally stable,contrary to what one might have expected.The possible implications of this result are discussed.Abbreviated title:Spectrum of Partial Locking in the Kuramoto Model1.IntroductionCollective synchronization occurs throughout the living world,from the rhythmic ﬁring of thousands of pacemaker cells in our hearts,to the chorusing of crickets on a warm summer evening[Winfree1967,1980;Pikovsky et al.2001;Strogatz2003].What is remarkable is that these and many other biological populations somehow manage to synchronize themselves spontaneously,without any external cue,despite the inevitable diversity in the natural frequencies of their constituent oscillators.Thirty years ago,Kuramoto introduced an elegant model of such self-synchronizing systems[Kuramoto1975,1984;for reviews,see Strogatz2000and Acebron et al.2005]. Although the model was originally inspired by biology[Winfree1967],it has since found application to many other parts of science and technology.Examples include the mutual synchronization of electrochemical oscillators[Kiss et al.2002],metronomes[Pantaleone 2002],Josephson junction arrays[Wiesenfeld,Colet and Strogatz1996],neutrinoﬂavor oscillations[Pantaleone1998],collective atomic recoil lasing[von Cube et al.2004],audi-ences clapping in unison[Neda2000],and crowds walking on wobbly footbridges[Strogatz et al.2005].Aside from its scientiﬁc applications,the model has also been an object of mathemat-ical interest.Its main virtue has always been its tractability.In the limit of an inﬁnite number of oscillators,one could“solve the model exactly,”in the physicists’sense,as long as one was willing to make some plausible assumptions about the stability and conver-gence properties of the solutions.Putting these assumptions on a more rigorous footing has,however,turned out to be problematic.Indeed,Kuramoto himself realized this from the start and was frank about it.For instance,in his1984book he presents an ingenious formal calculation and then draws attention to its limitations.Speciﬁcally,he shows that as the coupling between the oscil-lators is increased,the zero solution(corresponding to a completely desynchronized state) bifurcates supercritically to a nonzero solution(corresponding to a partially synchronized state)at a critical value of the coupling strength.He then remarks that the zero solution should be stable below threshold and unstable above it,but writes“Surprisingly enough, this seemingly obvious fact seems diﬃcult to prove”[Kuramoto1984,p.74].Similarly,he points out that the bifurcating solution is expected to be stable above threshold,though“Again,this fact appears to be diﬃcult to prove”[Kuramoto1984,p.75].In this paper we settle the second of these issues,namely,the stability of the par-tially synchronized state.Weﬁnd that this state is linearly neutrally stable,rather than asymptotically stable.This result may seem puzzling,but there is a precedent for it:the same neutral stability was already establishedﬁfteen years ago for the zero solution(now known as the incoherent state)for coupling strengths below the synchronization threshold [Strogatz and Mirollo1991].The question studied here may be of interest to readers working on stability analyses in other parts of nonlinear science,wherever continuity equations arise,such as kinetic theory,traﬃcﬂow,plasma physics,andﬂuid mechanics.The problem formulation involves a nonlinear partial integro-diﬀerential equation,one of whose stationary solutions(the partially locked state)contains both a smooth piece and a delta-function piece.To make sense of this,we need to work in an appropriate functional-analytic setting,and carry out the linear stability analysis in a space of suitable“generalized functions.”The resulting technical issues are new,at least in this context.They certainly did not arise in previous studies of the other stationary states of the Kuramoto model.For example,the stability of the incoherent state can be determined with standard methods,at both the linear[Strogatz and Mirollo1991,Crawford1994]and weakly nonlinear[Bonilla et al.1992,Crawford1994]levels.The problem is relatively straightforward because the incoherent state is described by a smooth(in fact,constant)density of oscillators in phase space.The fully locked state is similarly amenable to conventional techniques,as long as N isﬁnite.Its stability analysis can be handled with linear algebra[Aeyels and Rogge 2004,Mirollo and Strogatz2005]or Lyapunov functions[van Hemmen and Wreszinski1993, Jadbabaie et al.2004,Chopra and Spong2006],since theﬁnite-N locked state corresponds to aﬁxed point for an ordinary diﬀerential equation.Even the partially locked state is susceptible to familiar approaches,if one regularizes the Kuramoto model by adding noise terms to it[Sakaguchi1988];then the stability of partial locking at onset follows from the weakly nonlinear analyses mentioned above[Bonilla et al.1992,Crawford1994].But none of these simpliﬁcations are available for the problem studied here.Its thornier aspects stem from the combination of a continuum limit,the absence of noise, the need to work far from the onset of instability,and the singular nature of the partially locked state itself.We imagine that a similar mix of ingredients could crop up in stabilityproblems in other parts of nonlinear science,and hence may be of wider interest.The goal of this paper is threefold:set up the continuum limit of the Kuramoto model in a mathematically precise fashion;describe theﬁxed states for this model;and carry out the linear stability analysis at these states.The third of these is by far the most interesting to us,since it has potential to shed light on the still poorly understood dynamics of theﬁnite-N system[Strogatz2000,Balmforth and Sassi2000,Maistrenko et al.2005].Ultimately,we will achieve a complete understanding of the spectrum of the linearized evolution equation for theﬁxed states of greatest signiﬁcance,which we call special positiveﬁxed states.These are the only candidates for stability;the other stationary states turn out to be manifestly unstable.The organization follows accordingly.After reviewing the Kuramoto model to es-tablish notation(Section2),we describe its continuum limit(Section3)and classify its correspondingﬁxed states(Section4).Included here is the derivation of Kuramoto’s original self-consistency equation[Kuramoto1975,1984],which becomes rigorous in this setting.In Section5we develop the technical machinery needed to describe the tangent space of the model at aﬁxed state;this is the natural domain for the linear stability analysis.We analyze the continuous spectrum of the linearized model in Section6,and derive a characteristic equation whose roots give us the eigenvalues of the linearization in Section7.Finally in Section8we prove that the fully locked special positive states are linearly stable,but the partially locked special positive states are only neutrally stable, since the spectrum contains the entire imaginary axis!The implications of this result for theﬁnite-N model are far from clear,although this vaguely suggests that one should not expect to see any kind of exponential convergence to a stable conﬁguration in theﬁnite-N system in the range of coupling for which there is only partial locking.Before turning to the analytical development,we would like to add a personal note. When we began thinking about this stability problem around a decade ago,we found ourselves confused by a number of its features.As we had done on an earlier occasion [Strogatz et al.1992],we turned to John David Crawford for advice.J.D.was a brilliant mathematical physicist with expertise in bifurcation theory,plasma physics,and nonlin-ear science in general.He was also exceptionally generous and a natural teacher.We last saw him in the spring of1998at a conference on pattern formation at the Institute for Mathematics and its Applications in Minneapolis.A few years earlier he had beendiagnosed with Burkitt’s lymphoma,and when we saw him at the meeting,he was frail from chemotherapy but delighted to be able to renew old friendships and to join in the scientiﬁc discussions.In particular,he became curious about the stability problem that is the subject of this paper.The three of us spent a few afternoons working out some preliminary calculations.Tragically,J.D.passed away later that summer,at age44.He was very much in our minds as we gathered the fortitude toﬁnish this project,and we’re sure it would have been completed much sooner had J.D.still been on our team.We are honored to dedicate this work to his memory.2.The Kuramoto modelThe Kuramoto model is the system˙θi =ωi+Kω,we can go into a moving frame at frequencyω=0without lossof generality;thenﬁxed points of(1)correspond to phase-locked solutions in the original reference frame.We also assume that at least oneωi=0;otherwise,(1)is a gradientsystem and is very easy to analyze.To characterize the macroscopic state of the system,it is convenient to introduce a complex order parameter deﬁned byRe iψ=1Using the order parameter,we can rewrite the governing equations as˙θ=ωi+KR sin(ψ−θi),i=1,...,N.(2)iFor a given set of natural frequenciesω1,...,ωN there exists a locking threshold K l such that(1)hasﬁxed points(fully locked states)if and only if K≥K l;furthermore,for K>K l,(1)has a unique stableﬁxed point up to rotational symmetry,and hence has a unique stableﬁxed point whose order parameter has angleψ=0[Aeyels and Rogge2004, Mirollo and Strogatz2005].Equation(2)shows that K l≥|ωi|for all i,so K l will be large if just one of the natural frequenciesωi is large.So if the natural frequenciesωi are chosen randomly with respect to a probability density function g on R which has inﬁnite support, then as N→∞the system(1)will have noﬁxed points for most selections ofωi.Kuramoto’s intuition was that one could still predict the asymptotic behavior of the system(1)for large N in the absence ofﬁxed points.He guessed that as N→∞the order parameter might still settle down to an almost constant value,despite the incessant motion of the unlocked oscillators.Seeking such statistically steady solutions,one can assume the order parameter actually is a constant R>0and proceed from there.Then the oscillators divide into two classes,the locked and drifting oscillators,according to whether equation(2)has aﬁxed point or not;the locked oscillators have natural frequencies ωi∈[−KR,KR],whereas the drifting oscillators have|ωi|>KR.We call these kind of states partially locked,assuming there are in fact some drifting oscillators(otherwise we say the state is fully locked).Kuramoto showed that on average the drifting oscillators make no contribution to the order parameter R.Then,by computing the contribution from the locked oscillators,he produced a self-consistency equation for R.The N→∞limit of this equation has a solution R>0if and only if K is larger than some critical coupling K c,which Kuramoto computed in terms of the density function g.Numerical simulations later conﬁrmed that the size of the order parameter for the system(1)for large N remains close to the value of R predicted by Kuramoto’s self-consistency equation[Sakaguchi and Kuramoto1986].It’s important to understand that Kuramoto’s self-consistency equation is only a heuristic(albeit deeply insightful)calculation,so unfortunately no precise conclusions about theﬁnite-N system can be inferred from it.However,one can introduce an inﬁnite-N analogue of Kuramoto’s system,which has the advantage that the states analogous to thepartially locked conﬁgurations described above areﬁxed states in the inﬁnite-N model.We replace the oscillatorsθi and natural frequenciesωi with probability measuresρω,which we think of as describing the distribution of the oscillators with natural frequencyωon the circle S1.Hereωranges over the support of a density function g,so a state of the inﬁnite-N Kuramoto model is in eﬀect a family of probability measures parametrized by the natural frequenciesω.The measuresρωevolve according to an evolution equation mo-tivated by the conservation of oscillators;this is a continuity equation,or equivalently,a Fokker-Planck equation with no second-order(diﬀusion)term.In this setting,Kuramoto’s heuristic calculation can be made perfectly rigorous.3.The Inﬁnite-N Kuramoto ModelWe now describe the inﬁnite-N Kuramoto model.LetΩ=[−1,1]or R,and let g(ω) be a probability density function onΩ,which we think of as specifying a distribution of natural frequencies.We assume that g(−ω)=g(ω);g is non-increasing on[0,∞)∩Ω;and g is continuous onΩand nonzero on the interior ofΩ.Two familiar examples are the uniform density given by the constant function1/2on[−1,1],and the standard normal density function.(For convenience,we extend g to be0outsideΩin the caseΩ=[−1,1].) As we shall see,these conditions on g are necessary to facilitate many of the calculations undertaken in this paper.Let P r(S1)be the space of Borel probability measures on the unit circle.A state for the model will be a familyρω∈P r(S1),parametrized byω∈Ω.The mapω→ρωmustsatisfy at least a mild regularity condition,and to make sense of this we need to put a topology on the space P r(S1).There are various ways of doing this;we choose the one best suited to our purposes.Consider the Banach space C k(S1)of k-times continuously diﬀerentiable real-valued functions on the circle,where k is a non-negative integer(if k=0then C0(S1)=C(S1), the space of continuous functions on S1).The norm on C k(S1)can be deﬁned byφ k=maxθ∈S1 |φ(θ)|+|φ′(θ)|+···+|φ[k](θ)|forφ∈C k(S1).We’ll be working with the dual spaces C k(S1)∗throughout this paper, so it will be helpful to describe their elements as concretely as possible.Anyν∈C k(S1)∗can be represented as follows:φ,ν = S1φdµ0+ S1φ′dµ1+···+ S1φ[k]dµkwhereµ0,...,µk are signed Borel measures on S1andφis any C k function on S1(the signed measuresµ0,...,µk are not unique).We can express this more succinctly asφ,ν = 1,ν S1φdm+ S1φ[k]dµ(3) where m is normalized Lebesgue measure andµa signed Borel measure withµ(S1)= 0,which is now uniquely determined byν.The elements of C k(S1)∗can be thought of as a certain class of generalized functions or distributions on S1,which we call k th-order distributions;these are just measures and theirﬁrst k derivatives,in the sense of distributions.We can interpretν= 1,ν m+(−1)k D kµin this sense.In particular,a Borel probability measureµon S1is naturally an element of the dual space C k(S1)∗,with the pairing given by integration:φ,µ = S1φdµ.This gives an embedding of P r(S1)in C k(S1)∗,and we use the dual norm on C k(S1)∗to induce a metric on P r(S1).A distributionν∈C k(S1)∗is a probability measure if and only if 1,ν =1,and φ,ν ≥0for anyφ∈C k(S1)such thatφ≥0.This shows that P r(S1)is closed in C k(S1)∗for all k≥0.The inclusion map i:C k(S1)→C(S1)is a compact operator when k≥1,and hence so is its adjoint i∗:C(S1)∗→C k(S1)∗.Any probability measure has norm1when considered as an element of C(S1)∗,so P r(S1)is contained in the image of the unit ball under the map i∗,and hence P r(S1)is a compact subset of C k(S1)∗.From now on we insist that k≥1.The compactness of P r(S1)in C k(S1)∗has some desirable consequences.A compact Hausdorﬀtopology cannot be strengthened without sacriﬁcing compactness,or weakened without sacriﬁcing the Hausdorﬀproperty.This implies that the topology on P r(S1)is the same for all k.Furthermore,the so-called weak∗-topologies on C k(S1)∗all induce the same topology on P r(S1).The closure of the span of P r(S1)in C k(S1)∗is the subspace of elementsν∈C k(S1)∗that can be represented in the form(3)withµabsolutely continuous w.r.t.Lebesgue measure;we call this subspaceC k(S1)∗abs.The space C k(S1)∗abs is separable(it’s in fact isomorphic to L1(S1)),and so is an ideal choice for a Banach space in which to embed P r(S1).(The larger Banach spaces C k(S1)∗are not separable for all k≥0.)Now that we have a good topology on P r(S1),we can oﬃcially deﬁne the states of the inﬁnite-N Kuramoto model.We need a regularity condition on the states which will allow us to integrate various things;the mildest form of this is the requirement of measurability. So we deﬁne the states as follows:Deﬁnition.A state for the inﬁnite-N Kuramoto model is a measurable mapω→ρωfromΩto P r(S1).We denote the space of states by S.As is the usual practice,we shall identify two states which agree for almost allω∈Ω,so a state is actually an equivalence class of maps under this relation,but we will usually be tacit about this technicality.Since the weak∗and dual norm topologies on C k(S1)∗induce the same topology on P r(S1),the measurability condition is equivalent to requiring that for any C k functionφon S1,the functionω→ S1φdρωis measurable onΩ.The state space S is naturally a closed subset of the Banach space L1(Ω,C k(S1)∗abs)of(equivalence classes of)measurable functions fromΩto C k(S1)∗abs that are integrable with respect to the measure g(ω)dω.(See Lang[1993,Chapter VI]for background information on integration of functions with values in a Banach space).Let K>0be a constant,which we think of as determining the coupling strength for the model.The rest of the ingredients in the Kuramoto model can be deﬁned as follows. Deﬁnition.Given a stateρ∈S,its order parameter is the complex numberRe iψ= Ω 2π0e iθdρω(θ) g(ω)dω.(4) The vectorﬁeld vωassociated toρis the function vωon S1given byvω(θ)=ω+KR sin(ψ−θ).(5)Note that the mapω→ 2π0e iθdρω(θ)is a bounded measurable function ofω,and so the order parameter Re iψis well-deﬁned. The vectorﬁeld varies withω,so it’s best to think of this as a family of vectorﬁelds vωon S1parametrized byω∈R,just like the measuresρω.Now we canﬁnally describe the equation that drives the inﬁnite-N Kuramoto model:Deﬁnition.The evolution equation for statesρ∈S isd4.Fixed StatesOurﬁrst task is to determine theﬁxed states for our model.Aﬁxed stateρis just a solution to the equationD(vωρω)=0(for almost allω).The distributionsξon S1that satisfy Dξ=0are constant multiples of Lebesgue measure m on S1,which we normalize so that m(S1)=1.So theﬁxed states satisfy an equation of the formvωρω=Cωm,(7)where Cωis some coeﬃcient function depending onω.Ifρhas order parameter0then its associated vectorﬁeld reduces to vω(θ)=ω,so we see thatρω=m for allω.We call this ρthe incoherent state,as mentioned in the introduction.Note thatρdoes indeed have order parameter0,since 2πe iθdθ=0and so the inner integral in(4)is0for allω.Hence the incoherent state is the unique ﬁxed state with order parameter0.Now let’s try to understand theﬁxed states which have nonzero order parameter(there are a lot of them).Ifρis such a state,then so is the rotated stateρθ0given bydρθ0ω(θ)=dρω(θ−θ0),whereθ0is anyﬁxed angle.The order parameters forρθ0andρare related by the factor e iθ0,so we can narrow our search to states for which the order parameter has angleψ=0; in other words,we assume the order parameter is some R>0.Deﬁnition.The positiveﬁxed states are thoseﬁxed statesρ∈S for which the order parameter R>0.Plugging inψ=0givesvω(θ)=ω−KR sinθ.Letω∈Ω.If|ω|>KR,vω(θ)=0for allθ,and equation(7)givesCωdρω(θ)=Becauseρωis a probability measure,we must haveC−1ω= 2π0dθ2π2π |ω−KR sinθ|dθ.(9) It’s helpful to imagine that for these natural frequencies the oscillators are continuously distributed on the circle according to the measure deﬁned above;we call these oscillators or frequencies drifting for this reason.By the way,when K is suﬃciently large there exist positiveﬁxed states which have KR≥1(we’ll construct these in a moment).So when Ω=[−1,1],there existﬁxed states which have no drifting oscillators;we call these states fully locked.If|ω|≤KR we must have Cω=0in(7).To see this,observe that away from the zeros of vω,the measureρωis given bydρω(θ)=CωKR ,−π2;notice that this choice corresponds to the stableﬁxed point of the one-dimensionalﬂow on the circle deﬁned by˙θ=vω(θ)=ω−KR sinθ,for|ω|<KR with R regarded asﬁxed. The other root isθ∗ω=π−θω,and of course it corresponds to the unstableﬁxed point of theﬂow on the circle.Thusρωis just a sum of point masses at these two points.Let w(ω)be the weight of the probability measureρωat the pointθ∗ω.Our measurability assumption on the statesρωguarantees that w is a measurable function on[−KR,KR]∩Ω,taking values in[0,1]. The weight atθωis of course1−w(ω).So for|ω|≤KR we haveρω=(1−w(ω))δθω+w(ω)δθ∗ω,(10)where we useδθto denote the unit point mass measure at the pointθ.The case we are most interested in is when w(ω)=0a.e.;in other words,ρωis a unit point mass in the right half-plane(so in the general case,w measures the deviation from these preferred states).The intuition here is that these special states have the best chance of being stable for the full,inﬁnite-N system,since their locked oscillators are all located at their stable positions,at least with respect to perturbations that don’t change the order parameter. This observation motivates the following:Deﬁnition.The special positiveﬁxed states are thoseﬁxed statesρ∈S for which the order parameter R>0and the weight function w(ω)=0almost everywhere.Ifωis equal to either KR or−KR,then the only probability measureρωsatisfying (7)is a unit point mass atπ2,so the values of w at±KR are irrelevant.Of course technically we don’t even have to consider this case,since the stateρis completely determined if we describeρωfor almost allω.Since the frequencies|ω|≤KR have measure ρωconcentrated at one or two points,we call these oscillators or frequencies locked.Every positiveﬁxed state has some locked oscillators.If all oscillators are locked,we say the stateρis fully locked;of course,this can only happen whenΩ=[−1,1].Otherwise,we callρpartially locked.The stateρsatisﬁes the equationR= Ω 2π0e iθdρω(θ) g(ω)dω,which in terms of real and imaginary parts is equivalent toR= Ω 2π0cosθdρω(θ) g(ω)dωand0= Ω 2π0sinθdρω(θ) g(ω)dω.(11) We split each of these integrals according to whether|ω|≥KR or|ω|≤KR.In theﬁrst case we have 2π0cosθdρω(θ)=Cω 2π0cosθdθsince the integrand has a periodic antiderivative on S 1.We also have2π0sin θdρω(θ)=C ω2π0sin θdθKR2π0 1ω dθ=ω−2πC ωKR ,which is an odd function of ω.For the cosine integral we have2π0cos θdρω(θ)=(1−w (ω))cos(θω)+w (ω)cos(θ∗ω)=(1−2w (ω))KR 2.So R and w satisfy the self-consistency equationR =KR −KR (1−2w (ω)) KR 2g (ω)dω,or equivalentlyK −1= 1−1(1−2w (KRs ))Proposition1.To everyﬁxed stateρ∈S with order parameter R>0we associate a measurable weight function w:Ω∩[−KR,KR]→[0,1]that satisﬁes the self-consistency equation(12).Conversely,given R>0and a measurable function w:Ω∩[−KR,KR]→[0,1]which satisfy(12),the stateρdeﬁned by equations(9)and(10)is a positiveﬁxed state with order parameter R.Since most of our arguments treat the locked and drifting frequencies separately,we introduce notation for these sets;letΩl=Ω∩[−KR,KR]andΩd=Ω−Ωl.Now let’s look in more detail at the special positiveﬁxed states(where w=0);then(12) reduces to the simpler self-consistency equationK−1= 1−11−s2g(ts)ds=2 10.tSo the statesρ(t)are all identical up to a scaling of the frequencies.)f is continuous,positive,and non-increasing on[0,∞).We havef(0)=2g(0) 10 2,and lim t→∞f(t)=0.Therefore the image f((0,∞))is either 0,πg(0)2 ,depending on whether the valueπg(0)πg(0)such that(13)has solutions if K>K c,but not if K<K c.This is essentially Kuramoto’s derivation of the critical coupling value for his model.What happens at K=K c?It depends on the behavior of the density function g near0.Letω0be the largest value ofωsuch that g is constant on[0,ω].Ifω0>0(in other words,if g is locally constant at0)then the function f is constant on[0,ω0],so there is a family of solutions to(13)parametrized by t∈(0,ω0]which all have K=K c (Figure1(b)).However there are no solutions to(13)with K=K c and R>0when ω0=0(Figure1(a),(c)).If we rewrite the function R=tf(t)asR=2 t0 t 2g(ω)dω,then we see that R is a strictly increasing function of t,with image(0,1)for t>0.So if we plot the parametric curve(K,R)=(f(t)−1,tf(t))in the K-R plane,then we obtain a curve C in theﬁrst quadrant which deﬁnes R as an increasing,continuous function of K for K>K c,with perhaps a vertical segment at K=K c;R→1as K→∞(Figure1).Now suppose we have a positive solution(K0,R0)to(12)for a weight function w which is not almost everywhere equal to0.If we set t=K0R0,then(12)shows that K−10<f(t),so the point(K0,R0)will lie on the hyperbola KR=K0R0,in the region below the curve C and above the K-axis.Conversely,if(K0,R0)is in this region then we can construct a positiveﬁxed state with these parameters as follows.Let(K′0,R′0)be the point on C that intersects the hyperbola KR=K0R0.Take the special positiveﬁxed state with parameters(K′0,R′0)and continuously deform its weight function from w=0 to w=1/2;the correspondingﬁxed states’parameters will trace all points below C on the hyperbola KR=K0R0.To summarize,we see that for each point(K,R)on the curve C there corresponds a unique special positiveﬁxed state with parameters K and R;this state always has weight function w=0.And for each point(K,R)in the region between C and the K-axis thereexist(actually inﬁnitely many)positiveﬁxed states with those parameters;these states all have weight functions that are not a.e.equal to0.IfΩ=[−1,1],then the points(K,R) on or above the hyperbola KR=1correspond to fully locked states,whereas points below this hyperbola correspond to partially locked states(Figure1(a),(b)).So in this case there is a second critical coupling constantK l=f(1)−1such that the model has fully locked states if and only if K≥K l.(An equivalent formula for the locking threshold K l wasﬁrst obtained by Ermentrout[1985].)We wish to stress the distinction between K l and K c because there seems to be occasional confusion about it in the literature.To put it intuitively,suppose that K is gradually increased from zero.The system remains completely desynchronized until K reaches K c,at which point theﬁrst oscillators begin to phase-lock.Thus K c marks the onset of partial locking.With further increases in K,more and more drifting oscillators are recruited into the synchronized pack.When Kﬁnally reaches K l,the locking process is complete.Now all the oscillators run at the same frequency.Hence,partial locking begins at K c;full locking begins at K l.Notice that K l≥K c, with equality if and only if g is constant on[−1,1],corresponding to a uniform distribution of natural frequencies.If the support of g is R,full locking is never achieved,so it is natural to deﬁne K l=∞in this case(Figure1(c)).5.Linearization at Fixed StatesOur next task is to study the linearization of the evolution equation(6)at aﬁxed state ρ,which we assume is either a positiveﬁxed state or the incoherent state.Our ultimate goal is to describe the spectrum of this linearization,which if contained completely in the left half plane would establish the asymptotic stability of theﬁxed stateρin the nonlinear model.The domain of the linearized model will be the tangent space TρS atρof the state space S,which is a subspace of the Banach space L1(Ω,C k(S1)∗abs).We recall the relevant deﬁnitions.Deﬁnition.Suppose A be a subset of a(real)Banach space E,and p∈A.The tangent cone T C p A to A at p is the set of x∈E for which there exists a functionγ:[0,t0)→A。

出版社通信英语课件IOT物联网

initially 最初，首先 mechanism 机制，原理，结构 virtual 虚拟的参考译文：
物联网开始于1999年，其开始的设想是要连接虚拟世界与物理世界。
被动句翻译： •译成主动句 •译成无主句 •译成被动句：被、遭到，受到、给、叫、让---
长句的翻译：短句合并的翻译：定语从句的翻译：语态转换的翻译：名词从句的翻译：短语扩为句子的翻译：
achieve 获取，获得 not only but also recognition 识别，承认，认出 localization 地方化，定位 identify 识别，认出，确定
The RFID technology is the “speaking technology” for these things, therefore the RFID technology possessed an outstanding status in these key technologies.
definition 定义 refer to 涉及，指的是 object 物体，目标，对象 intelligent 智能的 recognition 识别，承认，认出 orientation trace 定向跟踪 peripheral 外围的，次要的；外围设备 infrared 红外线的；红外线 sensor 传感器 scanner 扫描器，扫描设备
significantly 意味深长的，重大的 manifestation 表示，显示，示威 incorporate 包含，吸收，合并 numerous 为数众多的，许多的 contemporary 同时代的，当代的

参考译文：然而，从早期一出现其发展就引人注目，现在
更是加入了跨行业的许多不同的应用内容，已经成为当下社会日常生活中非常重要的一部分。

Sejnowski Influence of ionic conductances on spike timing reliability of cortical neurons f

Inﬂuence of Ionic Conductances on Spike Timing Reliability of Cortical Neurons for Suprathreshold Rhythmic InputsSusanne Schreiber,1,5Jean-Marc Fellous,2Paul Tiesinga,1,3and Terrence J.Sejnowski1,2,41Sloan-Swartz Center for Theoretical Neurobiology,2Howard Hughes Medical Institute,and Computational Neurobiology Lab,Salk Institute,La Jolla,California92037;3Department of Physics and Astronomy,University of North Carolina,Chapel Hill,North Carolina 27599;4Department of Biology,University of California San Diego,La Jolla,California92037;and5Institute for Theoretical Biology, Humboldt-University Berlin,D-10115Berlin,GermanySubmitted9June2003;accepted inﬁnal form15September2003Schreiber,Susanne,Jean-Marc Fellous,Paul Tiesinga,and Ter-rence J.Sejnowski.Inﬂuence of ionic conductances on spike timing reliability of cortical neurons for suprathreshold rhythmic inputs.J Neurophysiol91:194–205,2004.First published September24, 2003;10.1152/jn.00556.2003.Spike timing reliability of neuronal responses depends on the frequency content of the input.We inves-tigate how intrinsic properties of cortical neurons affect spike timing reliability in response to rhythmic inputs of suprathreshold mean. Analyzing reliability of conductance-based cortical model neurons on the basis of a correlation measure,we show two aspects of how ionic conductances inﬂuence spike timing reliability.First,they set the preferred frequency for spike timing reliability,which in accordance with the resonance effect of spike timing reliability is well approxi-mated by theﬁring rate of a neuron in response to the DC component in the input.We demonstrate that a slow potassium current can modulate the spike timing frequency preference over a broad range of frequencies.This result is conﬁrmed experimentally by dynamic-clamp recordings from rat prefrontal cortical neurons in vitro.Second, we provide evidence that ionic conductances also inﬂuence spike timing beyond changes in preferred frequency.Cells with the same DCﬁring rate exhibit more reliable spike timing at the preferred frequency and its harmonics if the slow potassium current is larger and its kinetics are faster,whereas a larger persistent sodium current impairs reliability.We predict that potassium channels are an efﬁcient target for neuromodulators that can tune spike timing reliability to a given rhythmic input.I N T R O D U C T I O NIntrinsic neuronal properties,such as their biochemistry,the distribution of ion channels,and cell morphology contribute to the electrical responses of cells(see e.g.Goldman et al.2001; Magee2002;Mainen and Sejnowski1996;Marder et al.1996; Turrigiano et al.1994).In this study we explore the inﬂuence of ionic conductances on the reliability of the timing of spikes of cortical cells.Robustness of spike timing to physiological noise is the prerequisite for a spike timing–based code,and has recently been investigated(Beierholm et al.2001;Brette and Guigon2003;Fellous et al.2001;Fricker and Miles2000; Gutkin et al.2003;Mainen and Sejnowski1995;Reinagel and Reid2002;Tiesinga et al.2002).It has been found experimen-tally that different types of neurons are tuned to different stimuli with respect to spike timing reliability.For example, cortical interneurons show maximum reliability in response to higher-frequency sinusoidal stimuli,whereas pyramidal cells respond more reliably to lower-frequency sinusoidal inputs (Fellous et al.2001).An important difference between those types of neurons is the composition of their ion channels. Taking into account that effective numbers of ion channels can be adjusted on short time scales through neuromodulation, changes in ion channels may also provide a useful way for a neuron to dynamically maximize spike timing reliability ac-cording to the properties of the input.Spike timing reliability is enhanced with increasing stimulus amplitude(Mainen and Sejnowski1995).In the intermediate amplitude regime,the frequency content of the stimulus is an important factor determining reliability(Fellous et al.2001; Haas and White2002;Hunter and Milton2003;Hunter et al. 1998;Jensen1998;Nowak et al.1997;Tiesinga2002).Spike timing reliability of a neuron is maximal for those stimuli that contain frequencies matching the intrinsic frequency of a neu-ron(Hunter et al.1998).The intrinsic(or preferred)frequency is given by theﬁring rate of a neuron in response to the DC component of the stimulus.Because of the relation to the DC ﬁring rate of a neuron,both the DC value(whether the stimulus mean or additional synaptic input)and the conductances of a cell can be expected to inﬂuence the spike timing frequency preference.The former was recently shown by Hunter and Milton(2003).The inﬂuence of conductances(rather than injected current)on spike timing reliability through changes in the neuronal activity according to the resonance effect is the focus of theﬁrst part of this paper,see RESULTS(Inﬂuence of conductances on the frequency preference).In this part we speciﬁcally seek to understand which ionic conductances of cortical neurons can mediate changes of the preferred frequency(with respect to spike timing reliability) over a broad range of frequencies.Reliability is assessed on the basis of the robustness of spike timing to noise(of amplitude smaller than the stimulus amplitude).Injecting sinusoidal cur-rents on top of a DC current into conductance-based model neurons,we conﬁrm that spike timing reliability is frequency-dependent as predicted by the resonance effect.We show that reliability can be regulated at the level of ion channel popula-tions,and identify the slow potassium channels as powerful to inﬂuence the preferred frequency.Our simulations support that the inﬂuence of ion channels on spike timing reliability also holds for more realistic rhythmic stimulus waveforms.Dy-namic-clamp experiments in slices of rat prefrontal cortexAddress for reprint requests and other correspondence:T.J.Sejnowski, Computational Neurobiology Laboratory,The Salk Institute,10010N.Torrey Pines Road,La Jolla,CA92037(E-mail:terry@).The costs of publication of this article were defrayed in part by the payment of page charges.The article must therefore be hereby marked‘‘advertisement’’in accordance with18U.S.C.Section1734solely to indicate this fact.J Neurophysiol91:194–205,2004.First published September24,2003;10.1152/jn.00556.2003.con ﬁrm the theoretical prediction that slow potassium channels can mediate a change in spike timing reliability,dependent on the frequency of the input.In the second part of the RESULTS section (In ﬂuence of con-ductances on spike timing reliability at the preferred fre-quency )we explore the in ﬂuence of ion channels beyond changes in preferred frequency attributed to the resonance effect.Different neurons may have the same preferred fre-quency (i.e.,the same DC ﬁring rate)but different composition of ion channels.We analyze the in ﬂuence of slow potassium channels and persistent sodium channels on spike timing reli-ability for neurons with the same preferred frequency.We ﬁnd that both channel types signi ﬁcantly in ﬂuence spike timing reliability.Slow potassium channels increase reliability,whereas persistent sodium channels lower it.M E T H O D SModel cellsThe single-compartment conductance-based model neurons were implemented in NEURON.In the basic implementation,the neurons contained fast sodium channels (Na),delayed-recti ﬁer potassium channels (K dr ),leak channels (leak),slow potassium channels (K s ),and persistent sodium channels (Na P ).The time resolution of the numerical simulation was 0.1ms.The kinetic parameters of the 5basic channel types and reversal potentials were taken from a model of a cortical pyramidal cell Golomb and Amitai (1997),apart from the reversal potential of the leak channels,which was set to Ϫ80mV (to avoid spikes in the absence of input and noise).The conductances of the cell we will refer to as the reference cell were (in mS /cm 2):g Na ϭ24,g Kdr ϭ3,g leak ϭ0.02,g Ks ϭ1,and g NaP ϭ0.07(Golomb and Amitai 1997).Its input resistance was 186M ⍀.The slow potassium conductance represented potassium channels with an activation time on the order of several tens to hundreds of milliseconds (here 75ms).In the model it is responsible for a spike frequency adaptation to a current step,which is experimentally observed in cortical pyramidal neurons (Connors and Gutnick 1990;McCormick et al.1985).We also investigated cells where the K s channels were replaced by mus-carinic potassium channels (K M )and by calcium-dependent potassium channels (K Ca ).The muscarinic channel K M was a slow noninacti-vating potassium channel with Hodgkin –Huxley style kinetics (Barkai et al.1994;Storm 1990).The calcium-dependent conductance K Ca was based on ﬁrst-order kinetics and was responsible for a slow afterhyperpolarization (Tanabe et al.1998).This channel was acti-vated by intracellular calcium and did not depend on voltage.Because of the dependency of K Ca on calcium,we also inserted an L-type calcium channel as well as a simple Ca-ATPase pump and internal buffering of calcium.For the parameters of these additional currents see APPENDIX .Kinetic parameters of all channels used were set to 36°C.Stimulus waveformsThe stimuli used to characterize spike timing reliability of individ-ual cells consisted of 2components.The ﬁrst component was a constant depolarizing current I DC ,which was the same for all model cells (apart from the simulations designed to study of the in ﬂuence of the DC),and which also remained ﬁxed throughout experimental recording of a cell.The second component was a sine wave with frequency fi ͑t ͒ϭC sin ͓2␲f t ͔ϩI DCThe amplitude of the sine wave C was always smaller than I DC .Examples of stimuli are shown in Fig.1,B and C .To characterize spike timing reliability in model cells,we applied a set of such stimuli with 70different frequencies (1–70Hz in 1-Hz increments)and 3different amplitudes of the sine wave component (C ϭ0.05,0.1,and 0.15nA).I DC ϭ0.3nA in all cases.For each frequency and amplitude combination,spikes for n ϭ20repeated trials of the same stimulus (duration 2.0s)were recorded.Reliability was calculated based on spiking responses 500ms after the onset of the stimulus,discarding the initial transient.To simulate intrinsic noise,we also injected a different random zero-mean noise of small amplitude [SD ␴ϭ20pA]on each individual trial.For the reference cell the noise resulted in voltage ﬂuctuations of about 1.3mV SD at rest.The noise was generated from a Gaussian distribution and ﬁltered with an alpha function with a time constant of ␶ϭ3ms.Although overall reliability systematically decreased with the size of the noise,neither the frequency content of the noise nor the absolute size of the noise (in that range)signi ﬁcantly changed the results.Spike times were determined as the time when the voltage crossed Ϫ20mV from below.The input resistance for the model cells was estimated by application of a depolarizing DC current step suf ﬁciently large to depolarize the cell by Ն10mV.Model neurons were also tested with a stimulus where power was distributed around one dominant frequency.These more realistic stimuli were constructed to have a peak in the power spectrum in either the theta-or the gamma-frequency range.These waveforms mimic theta-and gamma-type inputs and were created by inverse Fourier transform of the power spectrum (with random phases).For the theta-rich wave,the power spectrum consisted of a large peak at 8Hz (Gaussian,␴ϭ1Hz)and a small peak at 50Hz (Gaussian,␴ϭ6Hz).For gamma-rich waves,the power spectrum had a large peak at 30or 50Hz (with ␴ϭ3and 6Hz,respectively),and a small peak at 8Hz (␴ϭ1Hz).These waveforms were ﬁrst normalized to have a root-mean-square (RMS)value of 1and were then used with different scaling factors (yielding different RMS values).The DC component was added after scaling.These stimuli were presented for 10s and when evaluating reliability,the ﬁrst 500ms after stimulus onset were discarded.The reliability measureSpike timing reliability was calculated from the neuronal responses to repeated presentations of the same stimulus.For the model studies this implied the same initial conditions,but different noise for each trial.Reliability was quanti ﬁed by a correlation-based measure,which relies on the structure of individual trials and does not require the de ﬁnition of a priori events.For a more detailed discussion of the method see Schreiber et al.(2003).The spike trains obtained from N repeated presentations of the same stimulus were smoothed with a Gaussian ﬁlter of width 2␴t ,and then pairwise correlated.The nor-malized value of the correlation was averaged over all pairs.The correlation measure R corr ,based on the smoothed spike trains,s ជi (i ϭ1,...,N ),isR corr ϭ2N ͑N Ϫ1͒͸i ϭ1N͸j ϭi ϩ1Ns ជi ⅐s ជj ͉s ជi ͉͉s ជj ͉The normalization guarantees that R corr ʦ[0;1].R corr ϭ1indicates the highest reliability and R corr ϭ0the lowest.For all model cell studies,␴t ϭ1.8ms and for the experimental data ␴t ϭ3ms.The value of ␴t for model cells was chosen such that,given the noise level,reliability values R corr exploited the possible range of its values [0;1],allowing for better discrimination between reliable and unreliable spike timing.The experimental data proved more noisy and therefore a larger ␴t was chosen to yield a good distinction between reliable and unreliable states.All evaluation of model and experimental data (beyond obtaining spike times)was performed in Matlab.195INFLUENCE OF IONIC CONDUCTANCES ON SPIKE TIMINGFiring rate analysisFor the ﬁring rate analysis,the full parameter space of Na,Na P ,K dr ,K s ,and leak conductances was analyzed.DC ﬁring rates were ob-tained for all possible parameter combinations within the parameter space of the 5conductances considered (see APPENDIX ).The maximum change in ﬁring rate achievable by one ion channel type was charac-terized (for each combination of the other 4conductances)as the difference between the maximum and minimum (nonzero)ﬁring rates achievable by variation of the ion channel conductance of interest,keeping the other 4conductances ﬁxed.If a cell never ﬁred despite variation in one conductance,it was excluded from the parameter space (Ͻ5%of the total 4-dimensional conductance space for any channel type tested).The distribution of maximum changes in ﬁring rate achievable by variation of the density of one ion channel type over all combinations of the other 4densities is presented in the paper.Experimental protocolsCoronal slices of rat prelimbic and infra limbic areas of prefrontal cortex were obtained from 2-to 4-wk-old Sprague-Dawley rats.Rats were anesthetized with Iso ﬂurane (Abbott Laboratories,North Chi-cago,IL)and decapitated.Brains were removed and cut into 350-␮m-thick slices using standard techniques.Patch-clamp was performed under visual control at 30–32°C.In most experiments Lucifer yellow (RBI,0.4%)or Biocytin (Sigma,0.5%)was added to the internal solution.In all experiments,synaptic transmission was blocked by D -2-amino-5-phosphonovaleric acid (D-APV;50␮M),6,7-dinitroqui-noxaline-2,3,dione (DNQX;10␮M),and biccuculine methiodide (Bicc;20␮M).All drugs were obtained from RBI or Sigma,freshly prepared in arti ﬁcial cerebrospinal ﬂuid,and bath applied.Whole cellpatch-clamp recordings were achieved using glass electrodes (4–10M ⍀)containing (in mM):KMeSO 4,140;Hepes,10;NaCl,4;EGTA,0.1;MgATP,4;MgGTP,0.3;phosphocreatine,14.Data were ac-quired in current-clamp mode using an Axoclamp 2A ampli ﬁer (Axon Instruments,Foster City,CA).Data were acquired using 2computers.The ﬁrst computer was used for standard data acquisition and current injection.Programs were written using Labview 6.1(National Instrument,Austin,TX)and data were acquired with a PCI16E1data acquisition board (National In-strument).Data acquisition rate was either 10or 20kHz.The second computer was dedicated to dynamic clamp.Programs were written using either a Labview RT 5.1(National Instrument)or a Dapview (Microstar Laboratory,Bellevue,WA)frontend and a C language backend.Dynamic clamp (Hughes et al.1998;Jaeger and Bower 1999;Sharp et al.1993)was implemented using a DAP5216a board (Microstar Laboratory)at a rate of 10kHz.A dynamic clamp was achieved by implementing a rapid (0.1-ms)acquisition/injection loop in current-clamp mode.All experiments were carried in accordance with animal protocols approved by the N.I.H.Stimuli consisted of sine waves of 30different frequencies (1–30Hz)presented for 2s.Only one amplitude was tested.No additional noise was injected.The ﬁrst 500ms were discarded for analysis of reliability.R E S U L T SSpike timing reliability of conductance-based model neu-rons was characterized using a sine wave stimulation protocol for model cells with different amounts of sodium,potassium,and leak conductances.The voltage response of thereferenceFIG .1.Reliability analysis.A :voltage response of the reference cell to a current step (I DC ϭ0.3nA).B and C :examples of stimuli (f ϭ9Hz,C ϭ0.05nA;f ϭ11Hz,C ϭ0.05nA,respectively).D and E :rastergrams of the spiking responses to the stimuli presented above.Reliability in D is low (R corr ϭ0.10);reliability in E is higher (R corr ϭ0.64).F :reliability as a function of frequency f and amplitude C ,of the sine component in the input (Arnold plot,in contrast to all following data calculated with 0.25-Hz resolution,based on 50trials each).Tongue-shaped regions of increased reliability are visible.Strongest tongue marks the resonant (or preferred)frequency of a cell.Rastergrams underlying reliability at positions D and E are those shown in panels D and E .G :DC ﬁring rate (I DC ϭ0.3nA)vs.the preferred frequency for all model cells derived from the reference cell.DC ﬁring rate is a good predictor of the preferred frequency.196SCHREIBER,FELLOUS,TIESINGA,AND SEJNOWSKImodel cell(see METHODS)to stimulation with a DC step current (I DCϭ0.3nA)is shown in Fig.1A.Model cells were stimulated with a set of sine waves on top of aﬁxed DC.Reliability values for each individual stimulus and cell,based on correlation of responses to repeated presen-tation of a stimulus each with an independent realization of the noise,were derived as a function of the frequency f and the amplitude of the sine component C.Figure1,B–E show examples of2stimuli used and responses to those stimuli obtained from the reference cell.Figure1F shows the complete set of reliability values as a function of frequency and ampli-tude of the sine component of the input.Distinct,tongue-shaped regions of high reliability,so-called Arnold tongues(Beierholm et al.2001),arising from the res-onance effect of spike timing reliability,are visible.Figure1F also shows that the degree of reliability depended on the power of the input at the resonant frequency of a neuron.The higher the amplitude at the resonant frequency,the more pronounced was the reliability.At high amplitudes,frequencies close to the resonant frequency also showed enhanced reliability.The Ar-nold tongues were approximately vertical,so that the fre-quency of maximum reliability showed only a weak depen-dency on the amplitude of the sine component.The difference in input frequency for maximal reliability,as the amplitude C varied from0.05to0.15nA,was usuallyϽ2Hz.In most examples presented in this study,the strongest resonance was found at a1:1locking to the stimulus,where one spike per cycle of the sine wave was elicited.Additional regions of enhanced reliability could be observed at harmonics of the main resonant frequency(1:2,1:3,and1:4phase locking,in order of decreasing strength),and at the1st subharmonic(2:1 phase locking).The location of the strongest Arnold tongue in frequency space revealed the preferred frequency of a neuron,which was well approximated by theﬁring rate of the neuron in response to the DC component alone.Figure1G shows a strong corre-lation between the preferred frequency(i.e.,position of the strongest Arnold tongue on the frequency axis determined by the frequency of highest reliability for a given amplitude,C) and the DCﬁring rate of a cell for a wide range of conductance values in the model(see APPENDIX).In all(but2)cases the resonant frequency was close to the DCﬁring ually,the resonant frequency at the lowest amplitude of the sine compo-nent was closest to the DCﬁring frequency.For the2outliers the highest value of reliability was achieved at the subhar-monic,or the1st harmonic of the DCﬁring frequency.The importance of the DCﬁring rate in generating phase-locked ﬁring patterns was previously emphasized(see e.g.Coombes and Bressloff1999;Hunter et al.1998;Keener et al.1981; Knight1972;Rescigno et al.1970).The resonant frequency is referred to as preferred frequency throughout the paper.Inﬂuence of conductances on the frequency preference Because ionic conductances are known to inﬂuence neuronal activity levels,we investigated the ability of ion channels to modulate the preferred frequency in theﬁrst part of this study. SIMULATION RESULTS FOR A CORTICAL SINGLE-COMPARTMENT MODEL CELL.We started from the model of a cortical neuron (the reference cell).First,we varied one channel density at a time,keeping the densities of the other channelsﬁxed.The Arnold plots of cells whose leak density and slow potassiumdensity were varied respectively are shown in Fig.2.Examplespike shapes(at DC stimulation)are shown next to the Arnoldplots.All cells showed a pronounced resonance—that is,a pro-nounced preferred frequency.For variation of the leak chan-nels,the preferred frequency shifted to slightly lower frequen-cies with increasing density of leak channels.In contrast tovariation in leak channels,variation of K s conductance showeda large shift in preferred frequency(see Fig.2B).We alsoexplored changes in preferred frequency induced by the otherconductances(i.e.,Na,K dr,and Na P).Preferred frequenciesyielding maximum reliability(at Cϭ0.1nA)as a function ofnormalized channel density are shown in Fig.3for all chan-nels,including leak and K s.Because each channel type operated in a different range ofdensities,some of which differed by orders of magnitude,wenormalized(for parameter range criteria see APPENDIX)thedensities to the range[0;1]for each channel type,respectively.For Na,K dr,and Na P large changes in densities were necessaryto shift the preferred frequency.The overall observed changefor these channel types was in the range of5to15Hz.Thusstarting from the reference cell,only variation in the K s densitycould shift the preferred frequency by several tens of Hertz,fromϽ10toϾ60Hz.In all cases studied,for a given channel density the reliabil-ity at the preferred frequency was also higher than it wouldhave been at this stimulus frequency for most other values ofchannel parably high values were achieved onlyfor channel densities where the frequency at the1st harmonicor the subharmonic Arnold tongue coincided with the stimulusfrequency.We also analyzed the inﬂuence of2other potassium chan-nels with slower kinetics on frequency preference of the ref-erence cell—a muscarinic potassium channel K M and a cal-cium-dependent potassium channel K Ca(for details see APPEN-DIX).For both cases,we substituted K s by the new potassium conductance,K M or K Ca,respectively.The results of the Ar-nold plot analysis are shown in Fig.3B.For both channel types,an increase of their conductance shifted the preferred fre-quency over a broad range of frequencies.The lowest achiev-able frequency at a given DC depended on the time constant ofthe slow potassium conductance.If2or more slow potassiumconductances were present at high densities,the broad tuningeffect was diminished and eventually suppressed at high con-ductance levels(data not shown).Figure3C presents the pre-ferred frequency as a function of K s conductance for different ␶Ks.The slower the kinetics of the K s channel,the lower the minimum achievable frequency and the broader the frequency range accessible through variation of the slow potassium con-ductance.For completeness we analyzed all combinations of Na,Na P,K dr,K s,and leak conductances.In this case,we relied on theDCﬁring rate as an estimate of the preferred frequency.Thedistribution of maximum changes inﬁring rate(i.e.,preferredfrequency)achievable by variation of the density of one ionchannel type over all combinations of the other4densities ispresented in Fig.4,which shows one curve for each ionchannel type.For a more detailed description of this analysissee METHODS.Variation of K s had a signiﬁcant effect on theﬁring frequency in almost all parameter regimes.Its inﬂuence197INFLUENCE OF IONIC CONDUCTANCES ON SPIKE TIMINGwas weakest when another potassium channel,K dr in this case,was present at high density.The mean change achieved with K s was around 20Hz.The mean change achieved by the other ion channels was Ͻ10Hz.The analysis also showed that,in principle,all ion channel types could achieve ﬁring rate changes of Ն20Hz.Within the parameter space investigated,this was true for only a minority of values of the other 4conductances.Figure 4B shows 4examples of parameter regimes where these channels signi ﬁ-cantly changed the preferred frequency.For example,this occurred for K dr when K s was not present or present only in small amounts.Na P could cause a large frequency shift when both potassium conductances,K dr and K s ,were low.Na was potent in changing the frequency when both potassium con-ductances and Na P were low.Its in ﬂuence in these cases weakened further with a higher density of leak channels.Leak channel variation also gave rise to higher frequency shifts when both potassium conductances were low and thesodiumFIG .2.In ﬂuence of leak and slow potassium conductances on spike timing reliability.A :right column of left panel shows Arnold reliability plots for 7different model cells,systematically varying in the amount of leak channels present (0,0.005,0.01,0.015,0.02,0.03,and 0.04mS/cm 2,top to bottom ).Left column :spikes of the corresponding cells in response to pure DC stimulation without intrinsic noise.Input resistance changed signi ﬁcantly with leak conductance over several hundreds of M ⍀.B :Arnold plots and spikes in response to DC stimulation for 7different model cells with increasing amounts of K s (0.05,0.15,0.3,0.6,1.0,1.5,and 2.0mS/cm 2,top to bottom ).Input resistance changed from about 230to 150M ⍀.For both panels the 3rd plot from the bottom (*)represented the reference cell (as in Fig.1F).FIG .3.Dependency of preferred frequency of the reference cell on individual channel densities.A :preferred frequency as a function of normalized channel density (see text for de ﬁnition),for 5different conductances.Variation in K s achieves the broadest shift in preferred frequency.B :preferred frequency for variation in a muscarinic potassium channel (K M )and a calcium-dependent potassium channel (K Ca )as a function of normalized channel density (based on sine wave reliability analysis).K M and K Ca ,respectively,replaced K s in the reference cell.C :DC ﬁring rate (an estimate of the preferred frequency)for K s channels of different time constants (␶Ks )as a function of K s peak conductance.Densities are not normalized in this panel.Lowest achievable frequency (at I DC ϭ0.3nA)depended on ␶Ks .198SCHREIBER,FELLOUS,TIESINGA,AND SEJNOWSKIconductances were not too large.In general,higher densities of leak channels tended to lower the minimum achievable fre-quency.To illustrate that regulation of ionic conductances on spiketiming reliability frequency preference would allow a cell to dynamically adjust its spike timing reliability,the effect of a temporary increase in K s conductance on spike timing reliabil-ity is presented in Fig.5.The conductance step was chosen such that the preferred frequency of the cell after the conduc-tance increase matched the stimulus frequency.Spike timing reliability during elevation of the K s conductance was signif-icantly enhanced.RELIABILITY OF INPUTS WITH MORE THAN ONE FREQUENCY.Many biologically relevant periodic inputs,such as inputs to neurons that participate in rhythms,exhibit a broad distribution of frequencies in their power spectrum.We therefore stimu-lated model neurons with quasi-random stimuli whose power spectrum contained 2peaks,one in the theta-range (about 8Hz)and one in the gamma range (30–70Hz).The 3rhythm-like stimuli tested are depicted in Fig.6.The reliability of a response to one of those stimuli depended on the amount of K s present in the neuron.For the theta-dominated input (Fig.6A )cells with higher K s conductances responded more reliably,whereas cells with lower K s conduc-tance (therefore tuned to higher frequencies)responded with lower reliability.For the gamma-dominated input,only cells with an optimally low K s conductance achieved a high reli-ability.A high K s conductance made the cell more unreliable.For all stimuli,the cell with preferred frequency (adjusted by K s )closest to the dominant frequency in the input yielded the highest spike timing reliability (as illustrated by the lower panels in Fig.6).Interestingly,the second (smaller)peak in the power spectra of the inputs was also re ﬂected by a small increase of reliability at corresponding densities of K s .Not surprisingly,reliability also tended to increase with the vari-ance (or RMS value),of the stimuli,across all stimuli and cells.EXPERIMENTAL RESULTS.To test the effects of slow potassiumchannels on preferred frequency physiologically,we per-formed patch-clamp recordings in slices of rat prefrontal cor-tex.We used the dynamic-clamp technique,which allows time-dependent currents to be injected that experimentally simulate conductances through on-line feedback.Thus we were able to arti ﬁcially introduce K s currents (with the same dynamics as the K s reference channel used in the modelsim-FIG .4.In ﬂuence of parameter variation on the preferred frequency.A :normalized distribution of frequency shifts (maximum changes in ﬁring rate)achievable by one ion channel type (measured over all combinations of the other 4channel types).Cells in conductance space that did not ﬁre were discarded.Different curves correspond to different ion channel types.B :4examples of cells where Na,Na P ,K leak ,and K dr could mediate large changes in preferred frequency (for parameters see APPENDIX ).Circles and solid lines indicate the preferred frequency derived with the sine wave protocol (C ϭ0.05nA);crosses indicate DC ﬁringrate.FIG .5.Dynamic changes in spike timing reliability attributed to conductance steps.A :superimposed voltage traces (n ϭ20)in response to a sine wave (f ϭ9Hz,C ϭ0.05nA),which is shown in D .K s conductance was temporarily increased,as indicated in B .C :rastergram of the responses.Parameters of the cell were those of the reference cell;g Ks values were 0.9and 1.4mS/cm 2;noise SD ␴ϭ0.03nA.Reliability (here estimated with ␴t ϭ3ms)changed from 0.18to 0.57at the conductance step and back to 0.17.199INFLUENCE OF IONIC CONDUCTANCES ON SPIKE TIMING。

专业英语期末复习

专业英语期末复习一．名词解释PCM pulse-code modulation 脉冲编码调制PPM Pulse Position Modulation 脉冲位置调制ASK amplitude shift keying (ASK) 幅移键控FSK frequency shift keying (FSK) 频移键控BFSK binary frequency shift keying 二进制频移键控MSK minimum shift keying 最小频移键控PSK phase shift keying (PSK) 相移键控FDM Frequency division multiplexing频分复用OFDM orthogonal frequency division multiplexing 正交频分复用TDM time division multiplexing 时分复用WDM wave division multiplexing 波分复用DWDM dense wave division multiplexing 密集型波分复用PM amplitude/ frequency/ phase modulation (AM/FM/PM)幅度/频/调制CPM continuous phase modulation 连续相位调制FDMA frequency division multiple access.频分多址TDMA time division multiple access 时分多址CDMA code division multiple access 码分多址SDMA space division multiple access 空分多址GSM global system for mobile communicatons 全球数字移动通信系统MS mobile station 移动台BTS base transceviver 基站收发台BSC base station controller 基站控制器BSS base station subsystem 基站子系统MSC mobile switching center 移动交换中心AUC Authentication center 鉴权中心VLR visitor location register 访问位置寄存器EIR equipment identity register 设备识别寄存器HLR home location register 本地位置寄存器PSTN public switched telephone network 公共电话交换网ISDN integrated sercices digital network 综合业务数字网Boardband—ISDN Boardband-ISDN ADSL asymmetric digital subscriber line 非对称数字用户线路NSS network and switching subsystem 网络交换中心PBX private branch exchange 程控交换机ATM asynchronous transfer mode 异步传输模式LAN local area network 局域网IEEE Institute of Electrical and Electronics Engineers美国电气和电子工程师协会CSMA/CD Carrier Sense Multiple Access/Collision Detect载波监听多路访问/冲突检测MAC medium access control 介质访问控制层LLC logical link control 链路逻辑控制TCP Transmission Control Protocol 传输控制协议FTP file transfer protocolJPEG: Joint Photographic Experts Group 联合图像专家小组MPEG: Moving Pictures Experts GroupNAP s network access points 网络接入点IXPs Internet exchange points 互联网接入点SNA systems network architecture 系统网络体系结构OSI open system interconnectionGPS thw global positioning system 全球定位系统ICMP：Internet Control Message Protocol控制报文协议IGMP：Internet Group Management Protocol 组管理协议FDD frequency division duplex 频分双工TDD time division duplex 时分双工PLL phase lock loop 锁相环ADC analog-to-digital converter模数转换器SSMA spread spectrum multiple access 扩频多址系统VLC variable length coding 可变长编码HDTV high-definition tevevisionVOD video-on-demand 视频点播技术OSS operation support systems 运营支撑系统DRM digital rights management 数字版权管理CISC/SISC complex/simple instruction set computerPLMN public land mobile network 公共陆地移动网MUL mobile user link 移动用户链路GWL gateway link 网关链路ISL inter satellite links 内部卫星链路BRI basic rate interface 基本速率接口PRI primary rate interface 基群速率接口TA terminal adapter 终端适配器APD avalanche photodiode 雪崩光电二极管PIN positive-intrinsic negative 本征光电二极管TE transverse electric mode模电模式TM tranaverse magnetic 横磁模式LP linearly polarized mode 线性模式STB set top box 机顶盒Multimedia 多媒体information theory 信息论signal-to-noise信噪比destination of the information信宿sequences of messages 消息序列the light intensity光强度three dimensional sound transmission三维声音传输In a multiplex PCM system the different speech functions must be sampled,compressed,quantized and encoded.在一个多路复用PCM系统中不同的语音函数必须被抽样、压缩、量化和编码a pair of wires一双金属丝a coaxial cable一条同轴缆a band of radio frequencies一波段的收音机频率a beam of light一束光discrete and continuous variables离散、连续变量modulated signal已调信号modulating signal 调制信号binary bit-steam二进制比特流base-band signal基带信号antennas.天线synchronization同步the carrier frequency载波频率Path-loss信道损耗penetration of obstacles绕射reflection反射, scattering散射, diffraction衍射Spectral efficiency 频率效率power efficiency功率效率robustenss稳定性DSP digital signal processor 数字信号处理器Multiple Access 多址技术the guard band 保护频段frequency hopping and direct sequence 调频和直接序列扩频downlink/uplink slots 上行时隙/下行时隙Circuit Switching 电路交换Packet switching 分组交换dedicate line 专用线路subscriber用户thunk 中继local loop 用户环路physical layer物理层datalink layer 数据链路层application layer 应用层Internetwork layer 网际层Network interface layer 网络接口层twisted copper cable双绞线coaxial cable 同轴电缆optical fiber 光缆Bus/tree/ring/star topology 总线/树/环/星型拓扑结构Round robin 循环reservation 预约contention 竞争an access point 接入点、访问点hierarchical 等级上hot spots 热点decompression/compression 解压缩/压缩encoder/decoder 编码器/解码器redundancy 冗余lossy/lossless 有损/无损multicast 多播authentication 身份鉴定/鉴权authoirization 授权nomadicity 漫游session management 会话管理stream control transmission 流控制传输协议channel bonding 信道绑定on hook/off hook 接通/挂断attenunation loss 衰减损耗transmission loss 传输损耗acousto optic modulator 声光调制器electro-optic modulator 光电调制器optical amplifiers 光放大器dielectric waveguide 电解质波导step inder fiber 阶跃光纤graded index fiber 渐变光纤single mode/multimode fibers 单/多模光纤hard/soft handover 硬/软切换spread spectrum 扩频narrowband signal/interference 窄带信号/干扰power density 功率谱密度resistance narrowband/adjacent interface 抵制窄带/频道干扰band pass filter 带通滤波器geostationary/geosynchronous satellite 同步卫星satellite for navigation 导航卫星Geostationary (or geosynchronous) earth orbit (GEO): 地球同步轨道Medium earth orbit (MEO): 中距离轨道Low earth orbit (LEO):近地轨道Highly elliptical orbit (HEO): 椭圆轨道paramount 及其simultaneously 同时mechanism 机制the radio spectrum 无线频谱a user process 一个用户进程defined by port and sockets 由端口号和套接字定义multiple application 多个应用程序duplicate data suppression 抑制数据复制error recovery 差错复原connection-orient reliable data delivery 面向连接的可靠的数据传输congestion/flow control 拥塞/流量控制二．翻译1.So What is Cloud Computing?We see Cloud Computing as a computing model, not a technology. In this model “customers” plug into the “cloud” to access IT resources which are priced and provided “on-demand”. Essentially, IT resources are rented and shared among multiple tenants much as office space, apartments, or storage spaces are used by tenants. Delivered over an Internet connection, the “cloud” replaces the company data center or server providing the same service. Thus, Cloud Computing is simply IT services sold and delivered over the Internet. Refer to section of Types of Cloud Computing.Cloud Computing vendors combine virtualization (one computer hosting several “virtual” servers), automated provisioning (servers have software installed automatically), and Internet connectivity technologies to provide the service[1]. These are not new technologies but a new name applied to a collection of older (albeit updated) technologies that are packaged, sold and delivered in a new way.A key point to remember is that, at the most basic level, your data resides on someone else’s server(s). This means that most concerns (and there are potentially hundreds) really come down to trust and control issues. Do you trust them with your data?那么什么是云计算?我们看到云计算作为一个计算模型,而不是技术。

XDXL 567 一款通用电 listened 产品说明书

XD567DIP8/XL567SOP8 1Features3DescriptionThe X D X L/567are general purpose tone•20to1Frequency Range With an Externaldecoders designed to provide a saturated transistor Resistorswitch to ground when an input signal is present •Logic Compatible Output With100-mA Current within the passband.The circuit consists of an I and Sinking Capability Q detector driven by a voltage controlled oscillatorwhich determines the center frequency of the •Bandwidth Adjustable From0to14%decoder.External components are used to •High Rejection of Out of Band Signals and Noiseindependently set center frequency,bandwidth and •Immunity to False Signals output delay.•Highly Stable Center Frequency•Center Frequency Adjustable from0.01Hz to500kHz2Applications•Touch Tone Decoding •Precision Oscillator•Frequency Monitoring and Control •Wide Band FSK Demodulation •Ultrasonic Controls•Carrier Current Remote Controls •Communications Paging Decoders 4Simplified Diagram5Device Comparison TableDEVICE NAME DESCRIPTIONX D X L/567General Purpose Tone Decoder6Pin Configuration and Functions8-PinPDIP(P)and SOIC(D)PackageTop ViewPin FunctionsPINTYPE DESCRIPTION NAME NO.GND7P Circuit ground.IN3I Device input.LF_CAP2I Loop filter capacitor pin(LPF of the PLL).OUT8O Device output.OF_CAP1I Output filter capacitor pin.T_CAP5I Timing capacitor connection pin.T_RES6I Timing resistor connection pin.VCC4P Voltage supply pin.7Specifications7.1Absolute Maximum Ratings(1)(2)(3)MIN MAX UNIT Supply Voltage Pin9V Power Dissipation(4)1100mWV815VV3−10VV3V4+0.5VX D X L/567070°CPDIP Package Soldering(10s)260°C Operating Temperature RangeVapor Phase(60s)215°CSOIC PackageInfrared(15s)220°C Storage temperature range,T stg−65150°C (1)Absolute Maximum Ratings indicate limits beyond which damage to the device may occur.Recommended Operating Conditions indicateconditions for which the device is functional,but do not ensure specific performance limits.Electrical Characteristics state DC and AC electrical specifications under particular test conditions which ensure specific performance limits.This assumes that the device is within the Recommended Operating Conditions.Specifications are not ensured for parameters where no limit is given,however,the typical value is a good indication of device performance.7.2Recommended Operating Conditionsover operating free-air temperature range(unless otherwise noted)MIN MAX UNITV CC Supply Voltage 3.58.5VV IN Input Voltage Level–8.58.5VT A Operating Temperature Range–20120°C7.3Thermal InformationXDXL/567THERMAL METRIC(1)D P UNIT8PINSRθJA Junction-to-ambient thermal resistance107.553.0RθJC(top)Junction-to-case(top)thermal resistance54.642.3RθJB Junction-to-board thermal resistance47.530.2°C/WψJT Junction-to-top characterization parameter10.019.6ψJB Junction-to-board characterization parameter47.030.1(1)For more information about traditional and new thermal metrics,see the IC Package Thermal Metrics application report,SPRA953.AC Test Circuit,T A=25°C,V+=5VXDXL/567XDXL/567PARAMETER TEST CONDITIONS UNITMIN TYP MAX MIN TYP MAXPower Supply Voltage Range 4.75 5.09.0 4.75 5.09.0V Power Supply Current Quiescent R L=20k68710mA Power Supply Current Activated R L=20k11131215mA Input Resistance18201520kΩSmallest Detectable Input Voltage I L=100mA,f i=f o20252025mVrms Largest No Output Input Voltage I C=100mA,f i=f o10151015mVrmsLargest Simultaneous Outband Signal to66dB Inband Signal RatioMinimum Input Signal to Wideband Noise B n=140kHz−6−6dB RatioLargest Detection Bandwidth121416101418%of f o Largest Detection Bandwidth Skew1223%of f oLargest Detection Bandwidth Variation with±0.1±0.1%/°C TemperatureLargest Detection Bandwidth Variation with 4.75–6.75V±1±2±1±5%V Supply VoltageHighest Center Frequency100500100500kHz Center Frequency Stability(4.75–5.75V)0<T A<7035±6035±60ppm/°C−55<T A<+12535±14035±140ppm/°C Center Frequency Shift with Supply Voltage 4.75V–6.75V0.5 1.00.4 2.0%/V4.75V–9V 2.0 2.0%/V Fastest ON-OFF Cycling Rate f o/20f o/20Output Leakage Current V8=15V0.01250.0125µAOutput Saturation Voltage e i=25mV,I8=30mA0.20.40.20.4Ve i=25mV,I8=100mA0.6 1.00.6 1.0Output Fall Time3030ns Output Rise Time150150nsFigure 2.Typical Bandwidth VariationFigure 1.Typical Frequency DriftFigure 4.Typical Frequency DriftFigure 3.Typical Frequency DriftFigure 5.Bandwidth vs Input Signal AmplitudeFigure rgest Detection BandwidthTypical Characteristics(continued)Figure7.Detection Bandwidth as a Function of C2and C3Figure8.Typical Supply Current vs Supply VoltageFigure9.Greatest Number of Cycles Before Output Figure10.Typical Output Voltage vs Temperature8Detailed Description8.1OverviewThe X D X L/567is a general purpose tone decoder.The circuit consists of I and Q detectors driven by a voltage controlled oscillator which determines the center frequency of the decoder.This device is designed to provide a transistor switch to ground output when the input signal frequency matches the center frequency pass band. Center frequency is set by an external timing circuit composed by a capacitor and a resistor.Bandwidth and output delay are set by external capacitors.8.2Functional Block DiagramDIPSOP。

低频磁场屏蔽问题简述

科技信息2013年第3期ＳＣＩＥＮＣＥ＆ＴＥＣＨＮＯＬＯＧＹＩＮＦＯＲＭＡＴＩＯＮ0引言近几十年来，人们对电磁场认识迅速提高，电磁防护也逐渐成为了科学界和普通民众共同关心的话题。

目前，人们对电磁防护的研究较多的集中在电场方面。

然而，研究发现，以磁场（尤其是低频磁场）为表现形式的电磁辐射所造成的危害也是相当大的。

低频磁场所造成的危害主要表现在以下几个方面：（1）在工业上，低频磁场干扰常用的电子电气设备的正常使用，例如铝电解槽中有数十KA 的电流，会在周围产生强大的磁场，这个磁场会使电流控制系统中的电子设备、工计算机等受到影响；（2）在医学上，研究发现，低频磁场对动物的生理会产生一定的影响。

研究报告表明，人体发生多种肿瘤癌变的概率与所受到的低频磁场辐射密切相关，长期处于低频磁场中工作的人患白血病的概率是普通人的6倍，患淋巴癌的概率是普通人的4倍；（3）低频磁场辐射有可能会造成国家重要经济、政治、军事等相关方面情报的泄漏，与国家安全问题密切相关。

因此研究低频磁场屏蔽问题，并且根据特定的环境提出相对应的解决方法，是非常有必要的。

1低频磁场相关概念磁场屏蔽是电磁屏蔽中的一个难题。

磁场屏蔽通常是指用于减少磁场向指定区域穿透的措施。

磁场可以分为两种，通常我们把频率大于100kHz 的磁场称之为高频磁场，把频率低于100kHz 的磁场称之为低频磁场。

1.1低频磁场屏蔽低频磁场屏蔽是指在磁场频率低于100kHz 时，采用某些屏蔽手段来保证指定区域不受外界低频磁场的干扰。

与高频磁场的屏蔽问题不同的是，在磁场的频率较低时，产生的磁场可能是各种几何构型导体中流过的电流导致的，也可能是周围铁磁材料的磁化引起的，另外加上屏蔽结构、屏蔽材料等原因，低频磁场的屏蔽相对更复杂一些。

1.2屏蔽效能电磁屏蔽效果通常用屏蔽效能来表示，低频磁场的屏蔽效果与此相同。

屏蔽效能SE B 定义为：SE B =B O (r )B S (r )其中，B O (r )表示当屏蔽不存在时，观察点r 处的磁感应强度；B S (r )表示当屏蔽存在时，观察点r 处的磁感应强度。

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LOCAL OSCILLATOR FOR A SCANNING
DOPPLER WIND
and
Jet Propulsion Laboratory
4800 Oak Grove Drive
Pasadena, CA911 09
USA
ABSTRACT
A compact cw
transmitter. This and an alternative diode laser LO
Robert
Jet Propulsion Laboratory
4800 Oak Grove Drive
Pasadena, CA 91109
USA
During the past year several advances have been made in the design and fabrication of a compact, modular
using a conical scan and nadir angle in the neighborhood of 30°.The laser is to be used as a local oscillator (LO) in a testbed 2-pm Doppler
The capability to tune the LO in synchronism with the conical scan azimuth angle, tracking the Doppler shift imposed on the signal backscattered from the atmosphere due to spacecraft motion, obviates the need for a photomixer-preamplifier combination which provides near quantum-noise limited performance throughout a 4-5 GHz bandwidth. At 350 km altitude the spacecraft velocity is approximately 7700 m S-l.If the nadir angle of the conical scan is 30°, the Doppler shift at the extrema (fore and aft pointing) positions are nearly
at the equator) introduces a frequency shift which is latitude dependent as well as azimuth scan angle dependent.
A schematic of the LO is shown in Figure 1, Although the basic cavity design is similar to that of the single-mode laser described previously [1,2], the cavity is much shorter, the output coupler is much smaller with reduced reflectance, and the
mode dimensions and the compact structure, In fact the optimum pump power at present is closer to 500
“Tunable frequency stabilized diode-laser-pumped
Tm, laser at room temperature” 32, 2082-2084(1993).
2.“Frequency Agile Diode Laser-Pumped
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-Diode-Laser r
I
Cavity
o
Crystal Temp.Controller
Laser Head Volume:。