2. Time-Domain Analysis of Continuous-Time Signals and Systems
连续刚构桥运营过程中跨中下挠的分析
持续刚构桥运营过程中跨中下挠旳分析摘要：对于目前持续刚构桥梁状况，对其运营过程中跨中下挠旳变化状况展开了考察，得出了某些因素，也给出了某些相应措施。
核心词：持续刚构桥，跨中下挠In the process of the continuous rigid frame bridge operation across themiddle and lower torsion analysisAbstract：For the case of continuous rigid frame bridge, in the process of its operations across the middle and lower torsion for inspection, the changes of some reasons, and gives some corresponding measures.Keywords: Continuous rigid frame bridge; Across the middle and lower scratching1 前言近来几十年，持续刚构桥梁在我国发展旳速度十分快。
由于使用强度高旳材料制作混凝土构件，可以大幅度减少截面尺寸，减少构造自重，对实现大跨径规定很有协助，但正由于如此桥跨旳变大，持续刚构桥在预定寿命年限中旳问题也暴露出来，一种不可忽视旳状况就是由于服役时间旳增长，如果持续刚构跨中旳大幅度下挠，必然引起桥梁在运作期内引起驾驶人员与乘车人员旳不适感，进一步威胁到车辆安全甚至车辆人员旳生命安全[1]。
持续刚构桥跨中下挠幅度过大，将导致梁体浮现裂缝，对构造整体安全产生威胁，因此大跨径持续刚构桥旳跨中下挠问题也成了这种类型旳桥梁在建设和发展过程中务必完善旳问题。
大跨径持续刚构桥旳明显病害之一便是跨中下挠问题，从目前来看跨径在80 m到100 m如下旳，病害较少；跨径在100 m 到160 m之间旳，病害多；而跨径在160 m以上旳，体现旳比较突出。
LK英文翻译
郑州轻工业学院本科毕业设计（论文）——英文翻译题目差错控制编码解决加性噪声的仿真学生姓名专业班级通信工程05-2 学号 12院（系）计算机与通信工程学院指导教师完成时间 2009年4月26日英文原文:Data communicationsGildas Avoine and Philippe OechslinEPFL, Lausanne, Switzerlandfgildas.avoine, philippe.oechsling@ep.chAbstractData communications are communications and computer technology resulting from the combination of a new means of communication. To transfer information between the two places must have transmission channel, according to the different transmission media, there is wired data communications and wireless data communications division. But they are through the transmission channel data link terminals and computers, different locations of implementation of the data terminal software and hardware and the sharing of information resources.1 The development of data communicationsThe first phase: the main language, through the human, horsepower, war and other means of transmission of original information.Phase II: Letter Post. (An increase means the dissemination of information)The third stage: printing. (Expand the scope of information dissemination)Phase IV: telegraph, telephone, radio. (Electric to enter the time)Fifth stage: the information age, with the exception of language information, there are data, images, text and so on.1.1 The history of modern data communicationsCommunication as a Telecommunications are from the 19th century, the beginning Year 30. Faraday discovered electromagnetic induction in 1831. Morse invented telegraph in 1837. Maxwell's electromagnetic theory in 1833. Bell invented the telephone in 1876. Marconi invented radio in 1895. Telecom has opened up in the new era. Tube invented in 1906 in order to simulate the development of communications.Sampling theorem of Nyquist criteria In 1928. Shannong theorem in 1948. The invention of the 20th century, thesemiconductor 50, thereby the development of digital communications. During the 20th century, the invention of integrated circuits 60. Made during the 20th century, 40 the concept of geostationary satellites, but can not be achieved. During the 20th century, space technology 50. Implementation in 1963 first synchronized satellite communications. The invention of the 20th century, 60 laser, intended to be used for communications, was not successful. 70 The invention of the 20th century, optical fiber, optical fiber communications can be developed.1.2 Key figuresBell (1847-1922), English, job in London in 1868. In 1871 to work in Boston. In 1873, he was appointed professor at Boston University. In 1875, invented many Telegram Rd. In 1876, invented the telephone. Lot of patents have been life. Yes, a deaf wife.Marconi (1874-1937), Italian people, in 1894, the pilot at his father's estate. 1896, to London. In 1897, the company set up the radio reported. In 1899, the first time the British and French wireless communications. 1916, implementation of short-wave radio communications. 1929, set up a global wireless communications network. Kim won the Nobel Prize. Took part in the Fascist Party.1.3 Classification of Communication SystemsAccording to type of information: Telephone communication system, Cable television system ,Data communication systems.Modulation by sub: Baseband transmission,Modulation transfer.Characteristics of transmission signals in accordance with sub: Analog Communication System ,Digital communication system.Transmission means of communication system: Cable Communications,Twisted pair, coaxial cable and so on.And long-distance telephone communication. Modulation: SSB / FDM. Based on the PCM time division multiple coaxial digital base-band transmission technology. Will gradually replace the coaxial fiber.Microwave relay communications:Comparison of coaxial and easy to set up, low investment, short-cycle. Analog phone microwave communications mainly SSB / FM /FDM modulation, communication capacity of 6,000 road / Channel. Digital microwave using BPSK, QPSK and QAM modulation techniques. The use of 64QAM, 256QAM such as multi-level modulation technique enhance the capacity of microwave communications can be transmitted at 40M Channel 1920 ~ 7680 Telephone Rd PCM figure.Optical Fiber Communication: Optical fiber communication is the use of lasers in optical fiber transmission characteristics of long-distance with a large communication capacity, communication, long distance and strong anti-interference characteristics. Currently used for local, long distance, trunk transmission, and progressive development of fiber-optic communications network users. At present, based on the long-wave lasers and single-mode optical fiber, each fiber road approach more than 10,000 calls, optical fiber communication itself is very strong force. Over the past decades, optical fiber communication technology develops very quickly, and there is a variety of applications, access devices, photoelectric conversion equipment, transmission equipment, switching equipment, network equipment and so on. Fiber-optic communications equipment has photoelectric conversion module and digital signal processing unit is composed of two parts.Satellite communications: Distance communications, transmission capacity, coverage, and not subject to geographical constraints and high reliability. At present, the use of sophisticated techniques Analog modulation, frequency division multiplexing and frequency division multiple access. Digital satellite communication using digital modulation, time division multiple road in time division multiple access.Mobile Communications: GSM, CDMA. Number of key technologies for mobile communications: modulation techniques, error correction coding and digital voice encoding. Data Communication Systems.1.4 Five basic types of data communication system:（1）Off-line data transmission is simply the use of a telephone or similar link to transmit data without involving a computer system.The equipment used at both ends of such a link is not part of a computer, or at least does not immediately make the data available for computer process, that is, the data when sent and / or received are 'off-line'.This type of data communication is relatively cheap and simple.（2）Remote batch is the term used for the way in which data communication technology is used geographically to separate the input and / or output of data from the computer on which they are processed in batch mode.（3）On-line data collection is the method of using communications technology to provide input data to a computer as such input arises-the data are then stored in the computer (say on a magnetic disk) and processed either at predetermined intervals or as required.（4）Enquiry-response systems provide, as the term suggests, the facility for a user to extract information from a computer.The enquiry facility is passive, that is, does not modify the information stored.The interrogation may be simple, for example, 'RETRIEVE THE RECORD FOR EMPLOYEE NUMBER 1234 'or complex.Such systems may use terminals producing hard copy and / or visual displays.（5）Real-time systems are those in which information is made available to and processed by a computer system in a dynamic manner so that either the computer may cause action to be taken to influence events as they occur (for example as in a process control application) or human operators may be influenced by the accurate and up-to-date information stored in the computer, for example as in reservation systems.2 Signal spectrum with bandwidthElectromagnetic data signals are encoded, the signal to be included in the data transmission. Signal in time for the general argument to show the message (or data) as a parameter (amplitude, frequency or phase) as the dependent variable. Signal of their value since the time variables are or not continuous, can be divided into continuous signals and discrete signals; according to whether the values of the dependent variable continuous, can be divided into analog signals and digital Signal.Signals with time-domain and frequency domain performance of the two most basic forms and features. Time-domain signal over time to reflect changing circumstances. Frequency domain characteristics of signals not only contain the same information domain, and the spectrum of signal analysis, can also be a clear understanding of the distribution ofthe signal spectrum and share the bandwidth. In order to receive the signal transmission and receiving equipment on the request channel, Only know the time-domain characteristics of the signal is not enough, it is also necessary to know the distribution of the signal spectrum. Time-domain characteristics of signals to show the letter .It’s changes over time. Because most of the signal energy is concentrated in a relatively narrow band, so most of our energy focused on the signal that Paragraph referred to as the effective band Bandwidth, or bandwidth. Have any signal bandwidth. In general, the greater the bandwidth of the signal using this signal to send data Rate on the higher bandwidth requirements of transmission medium greater. We will introduce the following simple common signal and bandwidth of the spectrum.More or less the voice signal spectrum at 20 Hz ~ 2000 kHz range (below 20 Hz infrasound signals for higher than 2000 KHz. For the ultrasonic signal), but with a much narrower bandwidth of the voice can produce an acceptable return, and the standard voice-frequency signal gnal 0 ~ 4 MHz, so the bandwidth of 4 MHz.As a special example of the monostable pulse infinite bandwidth. As for the binary signal, the bandwidth depends on the generalThe exact shape of the signal waveform, as well as the order of 0,1. The greater the bandwidth of the signal, it more faithfully express the number of sequences.3 The cut-off frequency channel with bandwidthAccording to Fourier series we know that if a signal for all frequency components can be completely the same through the transmission channel to the receiving end, then at the receiving frequency components of these formed by stacking up the signal and send the signal side are exactly the same, That is fully recovered from the receiving end of the send-side signals. But on the real world, there is no channel to no wear and tear through all the Frequency components. If all the Fourier components are equivalent attenuation, then the signal reception while Receive termination at an amplitude up Attenuation, but the distortion did not happen. However, all the transmission channel and equipment for different frequency components of the degree of attenuation is differentSome frequency components almost no attenuation, and attenuation of some frequency components by anumber, that is to say, channel also has a certain amount of vibrationIncrease the frequency characteristics, resulting in output signal distortion. Usually are frequency of 0 Hz to fc-wide channel at Chuan harmonic lost during the attenuation does not occur (or are a very small attenuation constant), whereas in the fc frequency harmonics at all above the transmission cross Decay process a lot, we put the signal in the transmission channel of the amplitude attenuation of a component to the original 0.707(that is, the output signal Reduce by half the power) when the frequency of the corresponding channel known as the cut-off frequency (cut - off frequency).Cut-off frequency transmission medium reflects the inherent physical properties. Other cases, it is because people interested in Line filter is installed to limit the bandwidth used by each user. In some cases, because of the add channel Two-pass filter, which corresponds to two-channel cut-off frequency f1 and f2, they were called up under the cut-off frequency and the cut-off frequency.This difference between the two cut-off frequency f2-f1 is called the channel bandwidth. If the input signal bandwidth is less than the bandwidth of channel, then the entire input signal Frequency components can be adopted by the Department of channels, which the letter Road to be the output of the output waveform will be true yet. However, if the input signal bandwidth greater than the channel bandwidth, the signal of a Frequency components can not be more on the channel, so that the signal output will be sent with the sending end of the signal is somewhat different, that is produced Distortion. In order to ensure the accuracy of data transmission, we must limit the signal bandwidth.4 Data transfer rateChannel maximum data transfer rate Unit time to be able to transfer binary data transfer rate as the median. Improve data transfer rate means that the space occupied by each Reduce the time that the sequence of binary digital pulse will reduce the cycle time, of course, will also reduce the pulse width.The previous section we already know, even if the binary digital pulse signal through a limited bandwidth channel will also be the ideal generated wave Shape distortion, and when must the input signal bandwidth, the smaller channel bandwidth, output waveformdistortion will be greater. Another angle Degree that when a certain channel bandwidth, the greater the bandwidth of the input signal, the output signal the greater the distortion, so when the data transmissionRate to a certain degree (signal bandwidth increases to a certain extent), in the on-channel output signal from the receiver could not have been Distortion of the output signal sent to recover a number of sequences. That is to say, even for an ideal channel, the limited bandwidth limit System of channel data transfer rate.At early 1924, H. Nyquist (Nyquist) to recognize the basic limitations of this existence, and deduced that the noise-free Limited bandwidth channel maximum data transfer rate formula. In 1948, C. Shannon (Shannon) put into the work of Nyquist 1 Step-by-step expansion of the channel by the random noise interference. Here we do not add on to prove to those now seen as the result of a classic.Nyquist proved that any continuous signal f (t) through a noise-free bandwidth for channel B, its output signal as a Time bandwidth of B continuous signal g (t). If you want to output digital signal, it must be the rate of g (t) for interval Sample. 2B samples per second times faster than are meaningless, because the signal bandwidth B is higher than the high-frequency component other than a letter has been Road decay away. If g (t) by V of discrete levels, namely, the likely outcome of each sample for the V level of a discrete one, The biggest channel data rate Rm ax as follows:Rmax = 2Blog 2 V (bit / s)For example, a 3000 Hz noise bandwidth of the channel should not transmit rate of more than 6,000 bits / second binary digital signal.In front of us considered only the ideal noise-free channel. There is noise in the channel, the situation will rapidly deteriorate. Channel Thermal noise with signal power and noise power ratio to measure the signal power and noise power as the signal-to-noise ratio (S ignal - to -- Noise Ratio). If we express the signal power S, and N express the noise power, while signal to noise ratio should be expressed as S / N. However, people Usually do not use the absolute value of signal to noise ratio, but the use of 10 lo g1 0S / N to indicate the units are decibels (d B). For the S / N equal 10 Channel, said its signal to noise ratio for the 1 0 d B; the same token, if the channel S / N equal to one hundred, then the signal to noiseratio for the 2 0 d B; And so on. S hannon noise channel has about the maximum data rate of the conclusions are: The bandwidth for the BH z, signal to noise ratio for the S / N Channel, the maximum data rate Rm ax as follows:Rmax = Blog 2 (1 + S / N) (bits / second)For example, for a bandwidth of 3 kHz, signal to noise ratio of 30 dB for the channel, regardless of their use to quantify the number of levels, nor Fast sampling rate control, the data transfer rate can not be greater than 30,000 bits / second. S h a n n o n the conclusions are derived based on information theory Out for a very wide scope, in order to go beyond this conclusion, like you want to invent perpetual motion machine, as it is almost impossible.It is worth noting that, S hannon conclusions give only a theoretical limit, and in fact, we should be pretty near the limit Difficult.SUMMARYMessage signals are (or data) of a magnetic encoder, the signal contains the message to be transmitted. Signal according to the dependent variable Whether or not a row of values, can be classified into analog signals and digital signals, the corresponding communication can be divided into analog communication and digital communication.Fourier has proven: any signal (either analog or digital signal) are different types of harmonic frequencies Composed of any signal has a corresponding bandwidth. And any transmission channel signal attenuation signals will, therefore, Channel transmission of any signal at all, there is a data transfer rate limitations, and this is Chengkui N yquist (Nyquist) theorem and S hannon (Shannon) theorem tells us to conclusions.Transmission medium of computer networks and communication are the most basic part of it at the cost of the entire computer network in a very Large proportion. In order to improve the utilization of transmission medium, we can use multiplexing. Frequency division multiplexing technology has many Road multiplexing, wave division multiplexing and TDM three that they use on different occasions.Data exchange technologies such as circuit switching, packet switching and packetswitching three have their respective advantages and disadvantages. M odem are at Analog phone line for the computer's binary data transmission equipment. Modem AM modulation methods have, FM, phase modulation and quadrature amplitude modulation, and M odem also supports data compression and error control. The concept of data communications Data communication is based on "data" for business communications systems, data are pre-agreed with a good meaning of numbers, letters or symbols and their combinations.参考文献[1]C.Y.Huang and A.Polydoros,“Two small SNR classification rules for CPM,”inProc.IEEE Milcom,vol.3,San Diego,CA,USA,Oct.1992,pp.1236–1240.[2]“Envelope-based classification schemes for continuous-phase binary Frequency-shift-keyed modulations,”in Pr oc.IEEE Milcom,vol.3,Fort Monmouth,NJ,USA,Oct.1994,pp. 796–800.[3]A.E.El-Mahdy and N.M.Namazi,“Classification of multiple M-ary frequency-shift keying over a rayleigh fading channel,”IEEE m.,vol.50,no.6,pp.967–974,June 2002.[4]Consulative Committee for Space Data Systems(CCSDS),Radio Frequency and Modulation SDS,2001,no.401.[5]E.E.Azzouz and A.K.Nandi,“Procedure for automatic recognition of analogue and digital modulations,”IEE mun,vol.143,no.5,pp.259–266,Oct.1996.[6]A.Puengn im,T.Robert,N.Thomas,and J.Vidal,“Hidden Markov models for digital modulation classification in unknown ISI channels,”in Eusipco2007,Poznan,Poland, September 2007,pp.1882–1885.[7]E.Vassalo and M.Visintin,“Carrier phase synchronization for GMSK signals,”I nt.J.Satell. Commun.,vol.20,no.6,pp.391–415,Nov.2002.[8]J.G.Proakis,Digital Communications.Mc Graw Hill,2001.[9]L.Rabiner,“A tutorial on hidden Markov models and selected applications in speechrecognition,”Proc.IEEE,vol.77,no.2,pp.257–286,1989.英文译文：数据通信Gildas Avoine and Philippe OechslinEPFL, Lausanne, Switzerlandfgildas.avoine, philippe.oechsling@ep.ch摘要数据通信是通信技术和计算机技术相结合而产生的一种新的通信方式。
signal and system 英文原版书
signal and system 英文原版书Title: An Overview of the Book "Signal and System"Introduction:The book "Signal and System" is an essential resource for anyone interested in understanding the fundamentals of signal processing and system analysis. It provides a comprehensive and in-depth exploration of the concepts, theories, and applications related to signals and systems. This article aims to provide a detailed overview of the book, highlighting its key points and relevance.I. Fundamental Concepts of Signals and Systems:1.1 Definition and Properties of Signals:- Explanation of signals as time-varying or spatially varying quantities.- Discussion on continuous-time and discrete-time signals.- Description of signal properties such as amplitude, frequency, and phase.1.2 Classification of Signals:- Overview of different types of signals including periodic, aperiodic, deterministic, and random signals.- Explanation of energy and power signals.- Introduction to common signal operations such as time shifting, scaling, and time reversal.1.3 System Classification and Properties:- Definition and classification of systems as linear or nonlinear, time-invariant or time-varying.- Explanation of system properties like causality, stability, and linearity.- Introduction to system representations such as differential equations, transfer functions, and state-space models.II. Time-Domain Analysis of Signals and Systems:2.1 Convolution and Correlation:- Detailed explanation of convolution and its significance in system analysis.- Discussion on correlation as a measure of similarity between signals.- Application of convolution and correlation in practical scenarios.2.2 Fourier Series and Transform:- Introduction to Fourier series and its representation of periodic signals.- Explanation of Fourier transform and its application in analyzing non-periodic signals.- Discussion on the properties of Fourier series and transform.2.3 Laplace Transform:- Overview of Laplace transform and its use in solving differential equations.- Explanation of the relationship between Laplace transform and frequency response of systems.- Application of Laplace transform in system analysis and design.III. Frequency-Domain Analysis of Signals and Systems:3.1 Frequency Response:- Definition and interpretation of frequency response.- Explanation of magnitude and phase response.- Analysis of frequency response using Bode plots.3.2 Filtering and Filtering Techniques:- Introduction to digital and analog filters.- Discussion on different filter types such as low-pass, high-pass, band-pass, and band-stop filters.- Explanation of filter design techniques including Butterworth, Chebyshev, and Elliptic filters.3.3 Sampling and Reconstruction:- Explanation of sampling theorem and its importance in signal processing.- Overview of sampling techniques and their impact on signal reconstruction.- Discussion on anti-aliasing filters and reconstruction methods.IV. System Analysis and Stability:4.1 System Response and Impulse Response:- Explanation of system response to different input signals.- Introduction to impulse response and its relationship with system behavior.- Analysis of system stability based on impulse response.4.2 Transfer Function and Frequency Domain Analysis:- Definition and interpretation of transfer function.- Explanation of frequency domain analysis using transfer function.- Application of transfer function in system design and analysis.4.3 Feedback Systems and Control:- Overview of feedback systems and their role in control theory.- Explanation of stability analysis and design using control theory.- Discussion on PID controllers and their applications.V. Applications of Signal and System Theory:5.1 Communication Systems:- Explanation of modulation techniques and their role in communication systems.- Overview of demodulation techniques and their significance.- Discussion on error control coding and channel equalization.5.2 Digital Signal Processing:- Introduction to digital signal processing and its applications.- Explanation of digital filters and their role in signal processing.- Overview of image and speech processing techniques.5.3 Signal Processing in Biomedical Engineering:- Application of signal processing in biomedical signal analysis.- Discussion on medical imaging techniques such as MRI and CT scans.- Explanation of signal processing methods used in ECG and EEG analysis.Conclusion:The book "Signal and System" provides a comprehensive and detailed exploration of the fundamental concepts, theories, and applications related to signals and systems. It covers a wide range of topics including signal classification, system analysis, frequency-domain analysis, stability, and various applications. By studying this book, readers can gain a solid understanding of signal and system theory, which is essential in various fields such as communication, digital signal processing, and biomedical engineering.。
荧光寿命测试技术-时域或频域
Which Fluorescence Lifetime System is Best for You?Why Measure Lifetimes?The information from a steady-state scan (a plot of fluorescence intensity versus wavelength) represents the averaged behavior of what occurs during the entire scan. Fluorescence itself, how-ever, occurs on the nanosecond timescale. There-fore, if you could take snapshots at that speed, you would learn much more about the mecha-nisms that lead to chemical or biochemical proc-esses—hence the appeal of lifetime spectro-fluorometers.For example, among the experiments possi-ble with lifetime instruments include: •Determination of the environment that the sample molecules inhabit, e.g., viscosity, pH, temperature, polarity, salvation, etc. •Uncovering the size and shape of the sample molecules, and the distances between differ-ent parts of the molecules.•Learning about the contributions of each component in a mixture of sample mole-cules, through time-resolved spectra of over-lapping emissions.How to Measure Fluorescence LifetimesThere are two complementary techniques of lifetime measurement: the time domain and the frequency domain.In the time domain (Fig.1), a short pulse of light excites the sample, and the subsequent fluo-rescence emission is recorded as a function of time. This usually occurs on the nanosecond timescale.In the frequency domain (Fig. 2), the sample is excited by a modulated source of light. The fluorescence emitted by the sample has a similar waveform, but is modulated and phase-shifted from the excitation curve. Both modulation (M) and phase-shift (φ) are determined by the life-time of the sample emission; that lifetime can be calculated from the observed modulation and phase-shift.Both of these domains yield equivalent data. But, as we shall see, each method has advantages for measurement under certain conditions. This Application Note examines the time and fre-quency domains in more detail, in order to help you decide more easily which technique suits your sample conditions.Fig. 1. Actual pulsed light-source (gray) and sample response (black), showing the grad-ual decay of fluorescence intensity with time.A single-exponential fit (dotted) gives a life-time of 1.309 ± 0.003 ns.Fig. 2. Excitation (black) and sample re-sponse (gray), illustrating the phase-angle shift (φ) and demodulation ratio (M).SPEX® Fluorescence GroupF-10Fluorescence Decay LawBoth the time- and frequency-domain meth-ods take advantage of the fluorescence decay law , which is based on first-order kinetics. The decay law postulates that if a population of mole-cules is instantaneously excited when photons are absorbed, then the excited population—and hence the fluorescence intensity as a function of time, I (t )—gradually decays to the ground state. Decay kinetics can be described byταte t I −=)(where α is the intensity at time t = 0, t is the time after the absorption, and τ is the lifetime, that is, when the fraction of the population of molecules in the excited state (and the fluorescence inten-sity) has decreased by a factor of 1/e, or ~37%. Note that before absorption, I (t ) = 0.This fluorescence decay law implies that all excited molecules exist in a homogenous envi-ronment, as is true for many single-exponential fluorescence lifetime standards in solution 1,2. Apart from such standards, however, single-ex-ponential decays are usually a real-life exception, because most populations of excited molecules do not exist in homogeneous environments, and can be influenced by various factors, including the presence of quenchers , energy-transfer proc-esses among members of the population, and dif-ferent rates of molecular rotation. Hence, in most instances, multi-exponential or non-exponential forms of the decay-law equation must be applied.Time DomainTime-domain measurements are based on the assumption that, when photons are absorbed, the molecules can be excited in an infinitely brief moment. This idea is commonly known as the delta or δ-pulse . The δ-pulse idea is used to in-terpret data obtained with real pulsed light-sources with measurable pulse-widths. In prac-tice, the time-dependent profile of the light-pulse is reconvolved with the decay-law function. Re-convolution assumes that the δ-pulses are con-tinuous functions, so that the observed decay is the convolution integral of the decays from all δ-pulses initiated during the finite pulse-width 3.Fig. 3. Time-Correlated Single-Photon-Counting fluorometer. A pulsed light Source excites the Sample repetitively. The sample emission is observed by a Detector, while the excitation flashes are detected by a syn-chronization module (SYNC). A constant-fraction discriminator (CFD) responds to only the first photon detected (small ar-rows)—independent of its amplitude—from the detector. This first photon from sample emission is the stop signal for the Time-to-Amplitude Converter (TAC). The excitation pulses trigger the start signals. The Multi-Channel Analyzer (MCA) records repetitive start-stop signals of the single-photon events from the TAC, to generate a histo-gram of photon counts as a function of time-channel units. The lifetime is calculated from this histogram.There are many ways to record time-domain data, such as streak cameras, boxcar integrators,19202122232425262728TIME, CHANNELSCumulative histogramMonochroma-Sample chamberand so forth. Most agree, however, that the method of single-photon counting is, by far, su-perior.T ime-C orrelated S ingle-P hoton C ounting (TCSPC) measurements are shown in Fig. 3. TCSPC uses a pulsed light-source and a circuit to detect single-photon events at a detector. In a repetitive series of many start-stop signals from the circuitry, a binned histogram in time chan-nels of single-photon counts is gradually gener-ated.TCSPC relies on a principle of Poissonian statistics, that only one photon can be counted at a time and in any one channel, to avoid skewing the time-dependent statistics in photon-pile-up. Pile-up thus limits the data-acquisition rate of TCSPC to a few (typically 1–2) percent of the repetition rate. In practice, the single-photon limit is not a major hindrance because the pile-up limit can be monitored during the experiment, and decay times with sufficient photon counts in can be obtained in seconds to minutes with repe-tition rates in the MHz range. In addition, the Poissonian nature of the statistics allows the data to be rigorously analyzed.Frequency DomainThe fluorescence decay parameters in the de-cay law’s impulse function may be obtained based on the relation of a sinusoidally modulated excitation beam to the fluorescence emission re-sponse (Fig. 2). The emission occurs at the same frequency as the excitation. Because of the loss of electron energy (Stokes’ shift) between exci-tation and emission, the emission waveform is demodulated and phase-shifted in comparison to the excitation. Thus the demodulation ratio (M) and phase-angle shift (φ) constitute two separate observable parameters that are both directly re-lated, via a Fourier transformation4, to the initial fluorescence intensity, α, and lifetime, τ, for a population of fluorophores.Frequency-domain measurements are best performed using M ulti-F requency C ross-C orre-lation phase-and-modulation (MFCC), shown in Fig. 4. A modulated beam excites the sample. The fluorescence emission is detected by a P ho-to M ultiplier T ube (PMT) modulated at the same base radio-frequency as the master plus a low cross-correlation frequency (a few Hz). The base-frequency signals are filtered to reveal the cross-correlation frequency signal, which con-tains all the same demodulation (M) and phase-angle shift (φ) information as the fluorescence emission.Fig. 4. Multi-Frequency Cross-Correlation fluorometer. An unmodulated light Source emits a spectrum of continuous-wave light. The excitation monochromator (Excit. Mono.) selects an excitation wavelength. An amplified (Amp 1) master synthesizer (Mas-ter) drives the Pockels cell (Pockels) at a base frequency, Rf, which modulates the excitation beam. The modulated beam ex-cites the Sample, causing the sample to emit modulated fluorescence also at the base Rf. An emission monochromator (Emis. Mono.) selects one wavelength of modulated fluorescence. The photomultiplier tube (PMT) is modulated by an amplified (Amp 2) slave synthesizer (Slave) at the base Rf plus a low-frequency cross-correla-tion note (∆f). The sample emission at Rf cancels the slave Rf+∆f frequencies to yield the ∆f signal containing the same phase-an-gle shift (φ) and demodulation ratio (M) as the Rf fluorescence.SampleExcit.AMPLITUDE∆fUsually the sample is scanned over a range (10–16) of frequencies because of the intrinsic limitations of resolving mixtures using only one frequency. In theory, for a single-exponential emitter, one should observe the same lifetime using the observed φ and M at any given fre-quency4,5. However, for mixtures of components, φ is biased towards the faster decay components and M is weighted toward the slower compo-nents. Hence, resolving separate fluorescence lifetime parameters for mixtures requires a range of frequencies to be statistically valid. On the other hand, the MFCC technique is not con-strained by the Poissonian single-photon detec-tion limits of TCSPC. Therefore, rapid acquisi-tion at a high signal-to-noise ratio to resolve complex mixtures is possible.Which Method is Best for Your Sample?In principle, both methods can yield identical results for a wide variety of experimental sam-ples and conditions. A user may choose one Spex®-IBH fluorescence lifetime instrument method over the other for a variety of reasons: The frequency domain, for example, is compatible with a strong, tunable continuous-wave xenon excitation source that seamlessly covers a wide spectral range. With the frequency domain, lifetimes as short as 10 picoseconds can be measured with a continuous source, tunable from the UV to the near-IR. All other conditions being equal, frequency domain is usually faster than time domain.Time-domain instruments have no conti-nuously tunable, pulsed source from the UV to IR, so the choice of excitation wavelength is more limited. Because of pulse-width, lifetimes are usually limited to no shorter than just under a nanosecond with a flash lamp, though they can operate at picosecond timeframes with inexpen-sive diode sources. On the other hand, TCSPC is compatible with precise and inexpensive pulsed light-emitting diodes and diode-laser sources. The single-photon detection method is preferred when photon emission is too weak for fre-quency-domain detection. There is a sacrifice in available wavelengths for UV excitation, impor-tant for some biological samples, when the flash lamp is used, and may be inconvenient and slow.Most important for you, Jobin Yvon, uniting Spex® and IBH, now offers both time- and fre-quency-domain instruments to optimize your re-search time and effort. The choice is yours. Copyright © 2004 Jobin Yvon, Inc.1 R.A. Lampert, et al., Anal. Chem.,55:68–73, 1983.2 J.R. Lakowicz, et al., J. Fluor., 1(2):87–93, 1991.3 G. Hungerford and D.J.S. Birch, Meas. Sci. Tech., 7:121–135, 1996.4 D.M. Jameson and T.L. Hazlett, Biophysical and Bio-chemical Aspects of Fluorescence Spectroscopy, Plenum Press, New York, pp. 105–133, 1991.5 E. Gratton, et al., Ann. Rev. Biophys. Bioeng., 13:105–124, 1984.In the USA:Jobin Yvon Inc.3880 Park Avenue, Edison, NJ 08820 In France: Japan: +81 (0) 3 58230140 Tel:+1-732-494-8660 16-18, rue du Canal China: +86 (0) 10 6849 2216 Fax: +1-732-549-5157 91165 Longjumeau cedex Germany: +49 (0) 89 462317-0 E-Mail: info@ Tel: +33 (0) 1 64 54 13 00 Italy: +39 0 2 576047621-800-533-5946Fax: +33 (0) 1 69 09 93 19 U.K.: +44 (0) 8204 8142。
5------第三章 连续LTI特征函数、傅里叶级数
k
y( t ) x( t ) * h( t ) x ( )h( t )d
t
a e
k
sk t
k
a
k
H ( sk )e sk t
2
LTI系统分析的基本方法
将输入信号表示成基本信号的线性组合： 时域法： x(t ) x( ) (t )d
从卷积的角度求输出： y (t ) x(t 3) x(t ) * (t 3) h(t ) (t 3)
s j 2
( 3)e s d
s j 2
e 3 s
s j 2
e j 6
方法二： （第六章）
H(s)
Yzs (s) 3s e X (s)
卷积定理
y (t ) e * h(t ) h( )e s ( t ) d
e e H ( s )
st LTI st
e
st
h( )e s d e st H ( s )
特征函数
特征值 （系统函数，传递函数）
H ( s ) h( )e s d h(t)的拉氏变换
例3-2 考虑输入x(t)和输出y(t)是个延时为3的LTI系统，即y(t)=x(t-3) 1）若输入为x(t)=ej2t，求输出及其特征值H(s)。 解：1)
y (t ) x(t 3) e j 2 ( t 3) e j 6 e j 2t
H ( s ) s j 2 h( )e s d
3
本章主要内容
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数学词汇中英文对照
数学词汇中英文对照abbreviation 简写符号；简写abscissa 横坐标absolute complement 绝对补集absolute error 绝对误差absolute inequality 绝不等式absolute maximum 绝对极大值absolute minimum 绝对极小值absolute monotonic 绝对单调absolute value 绝对值accelerate 加速acceleration 加速度acceleration due to gravity 重力加速度; 地心加速度accumulation 累积accumulative 累积的accuracy 准确度act on 施于action 作用; 作用力acute angle 锐角acute-angled triangle 锐角三角形add 加addition 加法addition formula 加法公式addition law 加法定律addition law(of probability) （概率）加法定律additive inverse 加法逆元; 加法反元additive property 可加性adjacent angle 邻角adjacent side 邻边adjoint matrix 伴随矩阵algebra 代数algebraic 代数的algebraic equation 代数方程algebraic expression 代数式algebraic fraction 代数分式；代数分数式algebraic inequality 代数不等式algebraic number 代数数algebraic operation 代数运算algebraically closed 代数封闭algorithm 算法系统; 规则系统alternate angle （交）错角alternate segment 内错弓形alternating series 交错级数alternative hypothesis 择一假设; 备择假设; 另一假设altitude 高；高度；顶垂线；高线ambiguous case 两义情况；二义情况amount 本利和；总数analysis 分析；解析analytic geometry 解析几何angle 角angle at the centre 圆心角angle at the circumference 圆周角angle between a line and a plane 直 与平面的交角angle between two planes 两平面的交角angle bisection 角平分angle bisector 角平分线 ；分角线angle in the alternate segment 交错弓形的圆周角angle in the same segment 同弓形内的圆周角angle of depression 俯角angle of elevation 仰角angle of friction 静摩擦角; 极限角angle of greatest slope 最大斜率的角angle of inclination 倾斜角angle of intersection 相交角；交角angle of projection 投射角angle of rotation 旋转角angle of the sector 扇形角angle sum of a triangle 三角形内角和angles at a point 同顶角angular displacement 角移位angular momentum 角动量angular motion 角运动angular velocity 角速度annum(X% per annum) 年（年利率X%）anti-clockwise direction 逆时针方向；返时针方向anti-clockwise moment 逆时针力矩anti-derivative 反导数; 反微商anti-logarithm 逆对数；反对数anti-symmetric 反对称apex 顶点approach 接近；趋近approximate value 近似值approximation 近似；略计；逼近Arabic system 阿刺伯数字系统arbitrary 任意arbitrary constant 任意常数arc 弧arc length 弧长arc-cosine function 反余弦函数arc-sin function 反正弦函数arc-tangent function 反正切函数area 面积Argand diagram 阿根图, 阿氏图argument (1)论证; (2)辐角argument of a complex number 复数的辐角argument of a function 函数的自变量arithmetic 算术arithmetic mean 算术平均；等差中顶；算术中顶arithmetic progression 算术级数；等差级数arithmetic sequence 等差序列arithmetic series 等差级数arm 边array 数组; 数组arrow 前号ascending order 递升序ascending powers of X X 的升幂assertion 断语; 断定associative law 结合律assumed mean 假定平均数assumption 假定；假设asymmetrical 非对称asymptote 渐近asymptotic error constant 渐近误差常数at rest 静止augmented matrix 增广矩阵auxiliary angle 辅助角auxiliary circle 辅助圆auxiliary equation 辅助方程average 平均；平均数；平均值average speed 平均速率axiom 公理axiom of existence 存在公理axiom of extension 延伸公理axiom of inclusion 包含公理axiom of pairing 配对公理axiom of power 幂集公理axiom of specification 分类公理axiomatic theory of probability 概率公理论axis 轴axis of parabola 拋物线的轴axis of revolution 旋转轴axis of rotation 旋转轴axis of symmetry 对称轴back substitution 回代bar chart 棒形图；条线图；条形图；线条图base （1）底；（2）基；基数base angle 底角base area 底面base line 底线base number 底数；基数base of logarithm 对数的底basis 基Bayes´theorem 贝叶斯定理bearing 方位（角）；角方向（角）bell-shaped curve 钟形图belong to 属于Bernoulli distribution 伯努利分布Bernoulli trials 伯努利试验bias 偏差；偏倚biconditional 双修件式; 双修件句bijection 对射; 双射; 单满射bijective function 对射函数; 只射函数billion 十亿bimodal distribution 双峰分布binary number 二进数binary operation 二元运算binary scale 二进法binary system 二进制binomial 二项式binomial distribution 二项分布binomial expression 二项式binomial series 二项级数binomial theorem 二项式定理bisect 平分；等分bisection method 分半法；分半方法bisector 等分线 ；平分线Boolean algebra 布尔代数boundary condition 边界条件boundary line 界（线）；边界bounded 有界的bounded above 有上界的；上有界的bounded below 有下界的；下有界的bounded function 有界函数bounded sequence 有界序列brace 大括号bracket 括号breadth 阔度broken line graph 折线图calculation 计算calculator 计算器；计算器calculus (1) 微积分学; (2) 演算cancel 消法；相消canellation law 消去律canonical 典型; 标准capacity 容量cardioid 心脏Cartesian coordinates 笛卡儿坐标Cartesian equation 笛卡儿方程Cartesian plane 笛卡儿平面Cartesian product 笛卡儿积category 类型；范畴catenary 悬链Cauchy sequence 柯西序列Cauchy´s principal value 柯西主值Cauchy-Schwarz inequality 柯西- 许瓦尔兹不等式central limit theorem 中心极限定理central line 中线central tendency 集中趋centre 中心；心centre of a circle 圆心centre of gravity 重心centre of mass 质量中心centrifugal force 离心力centripedal acceleration 向心加速度centripedal force force 向心力centroid 形心；距心certain event 必然事件chain rule 链式法则chance 机会change of axes 坐标轴的变换change of base 基的变换change of coordinates 坐标轴的变换change of subject 主项变换change of variable 换元；变量的换characteristic equation 特征(征)方程characteristic function 特征(征)函数characteristic of logarithm 对数的首数; 对数的定位部characteristic root 特征(征)根chart 图；图表check digit 检验数位checking 验算chord 弦chord of contact 切点弦circle 圆circular 圆形；圆的circular function 圆函数；三角函数circular measure 弧度法circular motion 圆周运动circular permutation 环形排列; 圆形排列; 循环排列circumcentre 外心；外接圆心circumcircle 外接圆circumference 圆周circumradius 外接圆半径circumscribed circle 外接圆cissoid 蔓叶class 区；组；类class boundary 组界class interval 组区间；组距class limit 组限；区限class mark 组中点；区中点classical theory of probability 古典概率论classification 分类clnometer 测斜仪clockwise direction 顺时针方向clockwise moment 顺时针力矩closed convex region 闭凸区域closed interval 闭区间coaxial 共轴coaxial circles 共轴圆coaxial system 共轴系coded data 编码数据coding method 编码法co-domain 上域coefficient 系数coefficient of friction 摩擦系数coefficient of restitution 碰撞系数; 恢复系数coefficient of variation 变差系数cofactor 余因子; 余因式cofactor matrix 列矩阵coincide 迭合；重合collection of terms 并项collinear 共线collinear planes 共线面collision 碰撞column (1)列；纵行；(2) 柱column matrix 列矩阵column vector 列向量combination 组合common chord 公弦common denominator 同分母；公分母common difference 公差common divisor 公约数；公约common factor 公因子；公因子common logarithm 常用对数common multiple 公位数；公倍common ratio 公比common tangent 公切 commutative law 交换律comparable 可比较的compass 罗盘compass bearing 罗盘方位角compasses 圆规compasses construction 圆规作图compatible 可相容的complement 余；补余complement law 补余律complementary angle 余角complementary equation 补充方程complementary event 互补事件complementary function 余函数complementary probability 互补概率complete oscillation 全振动completing the square 配方complex conjugate 复共轭complex number 复数complex unmber plane 复数平面complex root 复数根component 分量component of force 分力composite function 复合函数; 合成函数composite number 复合数；合成数composition of mappings 映射构合composition of relations 复合关系compound angle 复角compound angle formula 复角公式compound bar chart 综合棒形图compound discount 复折扣compound interest 复利；复利息compound probability 合成概率compound statement 复合命题; 复合叙述computation 计算computer 计算机；电子计算器concave 凹concave downward 凹向下的concave polygon 凹多边形concave upward 凹向上的concentric circles 同心圆concept 概念conclusion 结论concurrent 共点concyclic 共圆concyclic points 共圆点condition 条件conditional 条件句；条件式conditional identity 条件恒等式conditional inequality 条件不等式conditional probability 条件概率cone 锥；圆锥（体）confidence coefficient 置信系数confidence interval 置信区间confidence level 置信水平confidence limit 置信极限confocal section 共焦圆锥曲congruence (1)全等；(2)同余congruence class 同余类congruent 全等congruent figures 全等图形congruent triangles 全等三角形conic 二次曲 ; 圆锥曲conic section 二次曲 ; 圆锥曲conical pendulum 圆锥摆conjecture 猜想conjugate 共轭conjugate axis 共轭conjugate diameters 共轭轴conjugate hyperbola 共轭(直)径conjugate imaginary / complex number 共轭双曲 conjugate radical 共轭虚/复数conjugate surd 共轭根式; 共轭不尽根conjunction 合取connective 连词connector box 捙接框consecutive integers 连续整数consecutive numbers 连续数；相邻数consequence 结论；推论consequent 条件；后项conservation of energy 能量守恒conservation of momentum 动量守恒conserved 守恒consistency condition 相容条件consistent 一贯的；相容的consistent estimator 相容估计量constant 常数constant acceleration 恒加速度constant force 恒力constant of integration 积分常数constant speed 恒速率constant term 常项constant velocity 怛速度constraint 约束；约束条件construct 作construction 作图construction of equation 方程的设立continued proportion 连比例continued ratio 连比continuity 连续性continuity correction 连续校正continuous 连续的continuous data 连续数据continuous function 连续函数continuous proportion 连续比例continuous random variable 连续随机变量contradiction 矛盾converge 收敛convergence 收敛性convergent 收敛的convergent iteration 收敛的迭代convergent sequence 收敛序列convergent series 收敛级数converse 逆(定理)converse of a relation 逆关系converse theorem 逆定理conversion 转换convex 凸convex polygon 凸多边形convexity 凸性coordinate 坐标coordinate geometry 解析几何；坐标几何coordinate system 坐标系系定理；系；推论coplanar 共面coplanar forces 共面力coplanar lines 共面co-prime 互质; 互素corollary 系定理; 系; 推论correct to 准确至；取值至correlation 相关correlation coefficient 相关系数correspondence 对应corresponding angles (1)同位角；(2)对应角corresponding element 对应边corresponding sides 对应边cosecant 余割cosine 余弦cosine formula 余弦公式cost price 成本cotangent 余切countable 可数countable set 可数集countably infinite 可数无限counter clockwise direction 逆时针方向；返时针方向counter example 反例counting 数数；计数couple 力偶Carmer´s rule 克莱玛法则criterion 准则critical point 临界点critical region 临界域cirtical value 临界值cross-multiplication 交叉相乘cross-section 横切面；横截面；截痕cube 正方体；立方；立方体cube root 立方根cubic 三次方；立方；三次(的)cubic equation 三次方程cubic roots of unity 单位的立方根cuboid 长方体；矩体cumulative 累积的cumulative distribution function 累积分布函数cumulative frequecy 累积频数；累积频率cumulative frequency curve 累积频数曲cumulative frequcncy distribution 累积频数分布cumulative frequency polygon 累积频数多边形；累积频率直方图curvature of a curve 曲线的曲率curve 曲线curve sketching 曲线描绘(法)curve tracing 曲线描迹(法)curved line 曲线curved surface 曲面curved surface area 曲面面积cyclic expression 输换式cyclic permutation 圆形排列cyclic quadrilateral 圆内接四边形cycloid 旋输线; 摆线cylinder 柱；圆柱体cylindrical 圆柱形的damped oscillation 阻尼振动data 数据De Moivre´s theorem 棣美弗定理De Morgan´s law 德摩根律decagon 十边形decay 衰变decay factor 衰变因子decelerate 减速decelaration 减速度decile 十分位数decimal 小数decimal place 小数位decimal point 小数点decimal system 十进制decision box 判定框declarative sentence 说明语句declarative statement 说明命题decoding 译码decrease 递减decreasing function 递减函数；下降函数decreasing sequence 递减序列；下降序列decreasing series 递减级数；下降级数decrement 减量deduce 演绎deduction 推论deductive reasoning 演绎推理definite 确定的；定的definite integral 定积分definition 定义degenerated conic section 降级锥曲线degree (1) 度; (2) 次degree of a polynomial 多项式的次数degree of accuracy 准确度degree of confidence 置信度degree of freedom 自由度degree of ODE 常微分方程次数degree of precision 精确度delete 删除; 删去denary number 十进数denominator 分母dependence (1)相关; (2)应变dependent event(s) 相关事件; 相依事件; 从属事件dependent variable 应变量; 应变数depreciation 折旧derivable 可导derivative 导数derived curve 导函数曲线derived function 导函数derived statistics 推算统计资料; 派生统计资料descending order 递降序descending powers of x x的降序descriptive statistics 描述统计学detached coefficients 分离系数(法)determinant 行列式deviation 偏差; 变差deviation from the mean 离均差diagonal 对角线diagonal matrix 对角矩阵diagram 图; 图表diameter 直径diameter of a conic 二次曲线的直径difference 差difference equation 差分方程difference of sets 差集differentiable 可微differential 微分differential coefficient 微商; 微分系数differential equation 微分方程differential mean value theorem 微分中值定理differentiate 求...的导数differentiate from first principle 从基本原理求导数differentiation 微分法digit 数字dimension 量; 量网; 维(数)direct impact 直接碰撞direct image 直接像direct proportion 正比例direct tax, direct taxation 直接税direct variation 正变(分)directed angle 有向角directed line 有向直线directed line segment 有向线段directed number 有向数direction 方向; 方位direction angle 方向角direction cosine 方向余弦direction number 方向数direction ratio 方向比directrix 准线Dirichlet function 狄利克来函数discontinuity 不连续性discontinuous 间断(的);连续(的); 不连续(的) discontinuous point 不连续点discount 折扣discrete 分立; 离散discrete data 离散数据; 间断数据discrete random variable 间断随机变数discrete uniform distribution 离散均匀分布discriminant 判别式disjoint 不相交的disjoint sets 不相交的集disjunction 析取dispersion 离差displacement 位移disprove 反证distance 距离distance formula 距离公式distinct roots 相异根distincr solution 相异解distribution 公布distributive law 分配律diverge 发散divergence 发散(性)divergent 发散的divergent iteration 发散性迭代divergent sequence 发散序列divergent series 发散级数divide 除dividend (1)被除数；(2)股息divisible 可整除division 除法division algorithm 除法算式divisor 除数；除式；因子divisor of zero 零因子dodecagon 十二边形domain 定义域dot 点dot product 点积double angle 二倍角double angle formula 二倍角公式double root 二重根dual 对偶duality (1)对偶性; (2) 双重性due east/ south/ west /north 向东/ 南/ 西/ 北dynamics 动力学eccentric angle 离心角eccentric circles 离心圆eccentricity 离心率echelon form 梯阵式echelon matrix 梯矩阵edge 棱；边efficient estimator 有效估计量effort 施力eigenvalue 本征值eigenvector 本征向量elastic body 弹性体elastic collision 弹性碰撞elastic constant 弹性常数elastic force 弹力elasticity 弹性element 元素elementary event 基本事件elementary function 初等函数elementary row operation 基本行运算elimination 消法elimination method 消去法；消元法ellipse 椭圆ellipsiod 椭球体elliptic function 椭圆函数elongation 伸张；展empirical data 实验数据empirical formula 实验公式empirical probability 实验概率；经验概率empty set 空集encoding 编码enclosure 界限end point 端点energy 能; 能量entire surd 整方根epicycloid 外摆线equal 相等equal ratios theorem 等比定理equal roots 等根equal sets 等集equality 等(式)equality sign 等号equation 方程equation in one unknown 一元方程equation in two unknowns (variables) 二元方程equation of a straight line 直线方程equation of locus 轨迹方程equiangular 等角(的)equidistant 等距(的)equilateral 等边(的)equilateral polygon 等边多边形equilateral triangle 等边三角形equilibrium 平衡equiprobable 等概率的equiprobable space 等概率空间equivalence 等价equivalence class 等价类equivalence relation 等价关系equivalent 等价(的)error 误差error allowance 误差宽容度error estimate 误差估计error term 误差项error tolerance 误差宽容度escribed circle 旁切圆estimate 估计；估计量estimator 估计量Euclidean algorithm 欧几里德算法Euclidean geometry 欧几里德几何Euler´s formula 尤拉公式；欧拉公式evaluate 计值even function 偶函数even number 偶数evenly distributed 均匀分布的event 事件exact 真确exact differential form 恰当微分形式exact solution 准确解；精确解；真确解exact value 法确解；精确解；真确解example 例excentre 外心exception 例外excess 起exclusive 不包含exclusive disjunction 不包含性析取exclusive events 互斥事件exercise 练习exhaustive event(s) 彻底事件existential quantifier 存在量词expand 展开expand form 展开式expansion 展式expectation 期望expectation value, expected value 期望值；预期值experiment 实验；试验experimental 试验的experimental probability 实验概率explicit function 显函数exponent 指数exponential function 指数函数exponential order 指数阶; 指数级express…in terms of…以………表达expression 式；数式extension 外延；延长；扩张；扩充extension of a function 函数的扩张exterior angle 外角external angle bisector 外分角external point of division 外分点extreme point 极值点extreme value 极值extremum 极值face 面factor 因子；因式；商factor method 因式分解法factor theorem 因子定理；因式定理factorial 阶乘factorization 因子分解；因式分解factorization of polynomial 多项式因式分解fallacy 谬误FALSE 假(的)falsehood 假值family 族family of circles 圆族family of concentric circles 同心圆族family of straight lines 直线族feasible solution 可行解；容许解Fermat´s last theorem 费尔马最后定理Fibonacci number 斐波那契数；黄金分割数Fibonacci sequence 斐波那契序列fictitious mean 假定平均数figure (1)图(形)；(2)数字final velocity 末速度finite 有限finite dimensional vector space 有限维向量空间finite population 有限总体finite probability space 有限概率空间finite sequence 有限序列finite series 有限级数finite set 有限集first approximation 首近似值first derivative 一阶导数first order differential equation 一阶微分方程first projection 第一投影; 第一射影first quartile 第一四分位数first term 首项fixed deposit 定期存款fixed point 定点fixed point iteration method 定点迭代法fixed pulley 定滑轮flow chart 流程图focal axis 焦轴focal chord 焦弦focal length 焦距focus(foci) 焦点folium of Descartes 笛卡儿叶形线foot of perpendicular 垂足for all X 对所有Xfor each /every X 对每一Xforce 力forced oscillation 受迫振动form 形式；型formal proof 形式化的证明format 格式；规格formula(formulae) 公式four leaved rose curve 四瓣玫瑰线four rules 四则four-figure table 四位数表fourth root 四次方根fraction 分数；分式fraction in lowest term 最简分数fractional equation 分式方程fractional index 分数指数fractional inequality 分式不等式free fall 自由下坠free vector 自由向量; 自由矢量frequency 频数；频率frequency distribution 频数分布；频率分布frequency distribution table 频数分布表frequency polygon 频数多边形；频率多边形friction 摩擦; 摩擦力frictionless motion 无摩擦运动frustum 平截头体fulcrum 支点function 函数function of function 复合函数；迭函数functional notation 函数记号fundamental theorem of algebra 代数基本定理fundamental theorem of calculus 微积分基本定理gain 增益；赚；盈利gain perent 赚率；增益率；盈利百分率game （1）对策；（2）博奕Gaussian distribution 高斯分布Gaussian elimination 高斯消去法general form 一般式；通式general solution 通解；一般解general term 通项generating function 母函数; 生成函数generator (1)母线; (2)生成元geoborad 几何板geometric distribution 几何分布geometric mean 几何平均数；等比中项geometric progression 几何级数；等比级数geometric sequence 等比序列geometric series 等比级数geometry 几何；几何学given 给定；已知global 全局; 整体global maximum 全局极大值; 整体极大值global minimum 全局极小值; 整体极小值golden section 黄金分割grade 等级gradient (1)斜率；倾斜率；(2)梯度grand total 总计graph 图像；图形；图表graph paper 图表纸graphical method 图解法graphical representation 图示；以图样表达graphical solution 图解gravitational acceleration 重力加速度gravity 重力greatest term 最大项greatest value 最大值grid lines 网网格线group 组；grouped data 分组数据；分类数据grouping terms 并项；集项growth 增长growth factor 增长因子half angle 半角half angle formula 半角公式half closed interval 半闭区间half open interval 半开区间harmonic mean (1) 调和平均数; (2) 调和中项harmonic progression 调和级数head 正面（钱币）height 高（度）helix 螺旋线hemisphere 半球体；半球heptagon 七边形Heron´s formula 希罗公式heterogeneous (1)参差的; (2)不纯一的hexagon 六边形higher order derivative 高阶导数highest common factor(H.C.F) 最大公因子；最高公因式；最高公因子Hindu-Arabic numeral 阿刺伯数字histogram 组织图；直方图；矩形图Holder´s Inequality 赫耳德不等式homogeneous 齐次的homogeneous equation 齐次方程Hooke´s law 虎克定律horizontal 水平的；水平horizontal asymptote 水平渐近线horizontal component 水平分量horizontal line 横线 ；水平线 horizontal range 水平射程hyperbola 双曲线hyperbolic function 双曲函数hypergeometric distribution 超几何分布hypocycloid 内摆线hypotenuse 斜边hypothesis 假设hypothesis testing 假设检验hypothetical syllogism 假设三段论hypotrochoid 次内摆线idempotent 全幂等的identical 全等；恒等identity 等（式）identity element 单位元identity law 同一律identity mapping 恒等映射identity matrix 恒等矩阵identity relation 恒等关系式if and only if/iff 当且仅当；若且仅若if…, then 若….则；如果…..则illustration 例证；说明image 像点；像image axis 虚轴imaginary circle 虚圆imaginary number 虚数imaginary part 虚部imaginary root 虚根imaginary unit 虚数单位impact 碰撞implication 蕴涵式；蕴含式implicit definition 隐定义implicit function 隐函数imply 蕴涵；蕴含impossible event 不可能事件improper fraction 假分数improper integral 广义积分; 非正常积分impulse 冲量impulsive force 冲力incentre 内力incircle 内切圆inclination 倾角；斜角inclined plane 斜面included angle 夹角included side 夹边inclusion mapping 包含映射inclusive 包含的；可兼的inclusive disjunction 包含性析取；可兼析取inconsistent 不相的(的)；不一致(的) increase 递增；增加increasing function 递增函数increasing sequence 递增序列increasing series 递增级数increment 增量indefinite integral 不定积分idenfinite integration 不定积分法independence 独立；自变independent equations 独立方程independent event 独立事件independent variable 自变量；独立变量indeterminate (1)不定的；(2)不定元；未定元indeterminate coefficient 不定系数；未定系数indeterminate form 待定型；不定型index,indices 指数；指index notation 指数记数法induced operation 诱导运算induction hypothesis 归纳法假设inelastic collision 非弹性碰撞inequality 不等式；不等inequality sign 不等号inertia 惯性；惯量infer 推断inference 推论infinite 无限；无穷infinite dimensional 无限维infinite population 无限总体infinite sequence 无限序列；无穷序列infinite series 无限级数；无穷级数infinitely many 无穷多infinitesimal 无限小；无穷小infinity 无限(大)；无穷(大)inflection (inflexion) point 拐点；转折点inherent error 固有误差initial approximation 初始近似值initial condition 原始条件；初值条件initial point 始点；起点initial side 始边initial value 初值；始值initial velocity 初速度initial-value problem 初值问题injection 内射injective function 内射函数inner product 内积input 输入input box 输入inscribed circle 内切圆insertion 插入insertion of brackets 加括号instantaneous 瞬时的instantaneous acceleration 瞬时加速度instantaneous speed 瞬时速率instantaneous velocity 瞬时速度integer 整数integrable 可积integrable function 可积函数integral 积分integral index 整数指数integral mean value theorem 积数指数integral part 整数部份integral solution 整数解integral value 整数值integrand 被积函数integrate 积；积分；......的积分integrating factor 积分因子integration 积分法integration by parts 分部积分法integration by substitution 代换积分法；换元积分法integration constant 积分常数interaction 相互作用intercept 截距；截段intercept form 截距式intercept theorem 截线定理interchange 互换interest 利息interest rate 利率interest tax 利息税interior angle 内角interior angles on the same side of the transversal 同旁内角interior opposite angle 内对角intermediate value theorem 介值定理internal bisector 内分角internal division 内分割internal energy 内能internal force 内力internal point of division 内分点interpolating polynomial 插值多项式interpolation 插值inter-quartile range 四分位数间距intersect 相交intersection (1)交集；(2)相交；(3)交点interval 区间interval estimation 区间估计；区域估计intuition 直观invalid 失效；无效invariance 不变性invariant (1)不变的；(2)不变量；不变式inverse 反的；逆的inverse circular function 反三角函数inverse cosine function 反余弦函数inverse function 反函数；逆函数inverse cosine function 反三角函数inverse function 反函数；逆映射inverse mapping 反向映射；逆映射inverse matrix 逆矩阵inverse problem 逆算问题inverse proportion 反比例；逆比例inverse relation 逆关系inverse sine function 反正弦函数inverse tangent function 反正切函数inverse variation 反变(分)；逆变(分)invertible 可逆的invertible matrix 可逆矩阵irrational equation 无理方程irrational number 无理数irreducibility 不可约性irregular 不规则isomorphism 同构isosceles triangle 等腰三角形iterate (1)迭代值; (2)迭代iteration 迭代iteration form 迭代形iterative function 迭代函数iterative method 迭代法jet propulsion 喷气推进joint variation 联变(分)；连变(分)kinetic energy 动能kinetic friction 动摩擦known 己知L.H.S. 末项L´Hospital´s rule 洛必达法则Lagrange interpolating polynomial 拉格朗日插值多项代Lagrange theorem 拉格朗日定理Lami´s law 拉密定律Laplace expansion 拉普拉斯展式last term 末项latent root 本征根; 首通径lattice point 格点latus rectum 正焦弦; 首通径law 律；定律law of conservation of momentum 动量守恒定律law of indices 指数律；指数定律law of inference 推论律law of trichotomy 三分律leading coefficient 首项系数leading diagonal 主对角线least common multiple, lowest common multiple (L.C.M) 最小公倍数；最低公倍式least value 最小值left hand limit 左方极限lemma 引理lemniscate 双纽线length 长(度)letter 文字；字母like surd 同类根式like terms 同类项limacon 蜗牛线limit 极限limit of sequence 序列的极限limiting case 极限情况limiting friction 最大静摩擦limiting position 极限位置line 线；行line of action 作用力线line of best-fit 最佳拟合line of greatest slope 最大斜率的直 ；最大斜率line of intersection 交线line segment 线段linear 线性；一次linear convergence 线性收敛性linear differeantial equation 线性微分方程linear equation 线性方程；一次方程linear equation in two unknowns 二元一次方程；二元线性方程linear inequality 一次不等式；线性不等式linear momentum 线动量linear programming 线性规划linearly dependent 线性相关的linearly independent 线性无关的literal coefficient 文字系数literal equation 文字方程load 负荷loaded coin 不公正钱币loaded die 不公正骰子local maximum 局部极大(值)local minimum 局部极小(值)locus, loci 轨迹logarithm 对数logarithmic equation 对数方程logarithmic function 对数函数logic 逻辑logical deduction 逻辑推论；逻辑推理logical step 逻辑步骤long division method 长除法loop 回路loss 赔本；亏蚀loss per cent 赔率；亏蚀百分率lower bound 下界lower limit 下限lower quartile 下四分位数lower sum 下和lower triangular matrix 下三角形矩阵lowest common multiple(L.C.M) 最小公倍数machine 机械Maclaurin expansion 麦克劳林展开式Maclaurin series 麦克劳林级数magnitude 量；数量；长度；大小major arc 优弧；大弧major axis 长轴major sector 优扇形；大扇形major segment 优弓形；大弓形mantissa 尾数mantissa of logarithm 对数的尾数；对数的定值部many to one 多个对一个many-sided figure 多边形many-valued 多值的map into 映入map onto 映上mapping 映射marked price 标价Markov chain 马可夫链mass 质量mathematical analysis 数学分析mathematical induction 数学归纳法mathematical sentence 数句mathematics 数学matrix 阵; 矩阵matrix addition 矩阵加法matrix equation 矩阵方程matrix multiplication 矩阵乘法matrix operation 矩阵运算maximize 极大maximum absolute error 最大绝对误差maximum point 极大点maximum value 极大值mean 平均(值)；平均数；中数mean deviation 中均差；平均偏差mean value theorem 中值定理measure of dispersion 离差的量度measurement 量度mechanical energy 机械能median (1)中位数；(2)中线meet 相交；相遇mensuration 计量；求积法method 方法method of completing square 配方法method of interpolation 插值法; 内插法method of least squares 最小二乘法; 最小平方法method of substitution 代换法；换元法method of successive substitution 逐次代换法; 逐次调替法method of superposition 迭合法metric unit 十进制单位mid-point 中点mid-point formula 中点公式mid-point theorem 中点定理million 百万minimize 极小minimum point 极小点minimum value 极小值Minkowski Inequality 闵可夫斯基不等式minor (1)子行列式；(2)劣；较小的minor arc 劣弧；小弧minor axis 短轴minor of a determinant 子行列式minor sector 劣扇形；小扇形minor segment 劣弓形；小弓形minus 减minute 分mixed number(fraction) 带分数modal class 众数组mode 众数model 模型modulo (1)模; 模数; (2)同余modulo arithmetic 同余算术modulus 模; 模数modulus of a complex number 复数的模modulus of elasticity 弹性模(数)moment arm (1)矩臂; (2)力臂moment of a force 力矩moment of inertia 贯性矩momentum 动量monomial 单项式monotone 单调monotonic convergence 单调收敛性monotonic decreasing 单调递减monotonic decreasing function 单调递减函数monotonic function 单调函数monotonic increasing 单调递增monotonic increasing function 单调递增函数motion 运动movable pulley 动滑轮multinomial 多项式multiple 倍数multiple angle 倍角multiple-angle formula 倍角公式multiple root 多重根multiplicand 被乘数multiplication 乘法multiplication law (of probability) (概率)乘法定律multiplicative inverse 乘法逆元multiplicative property 可乘性multiplicity 重数multiplier 乘数；乘式multiply 乘multi-value 多值的mulually disjoint 互不相交mutually exclusive events 互斥事件mutually independent 独立; 互相独立mutually perpendicular lines 互相垂直n factorial n阶乘n th derivative n阶导数n th root n次根；n次方根n the root of unity 单位的n次根Napierian logarithm 纳皮尔对数; 自然对数natural logarithm 自然对数natural number 自然数natural surjection 自然满射necessary and sufficient condition 充要条件necessary condition 必要条件negation 否定式negative 负negative angle 负角negative binomial distribution 负二项式分布negative index 负指数negative integer 负整数negative number 负数negative vector 负向量; 负矢量neighborhood 邻域net 净(值)net force 净力Newton-Cote´s rule 牛顿- 高斯法则Newton-Raphson´s method 牛顿- 纳逊方法Newton´s formula 牛顿公式Newton´s law of motion 牛顿运动定律Newton´s method 牛顿方法n-gon n边形nonagon 九边形non-collinear 不共线non-commutative 非交换的non-linear 非线性。
ch2 linear time-invariant systems线性时不变系统
Ch2. Linear Time-Invariant Systems
hn un
Determine and plot the output y[n] x[n] h[n]
右移,
n>0，有重合
0 r
yn
1 2 k 令r k 2 k r 0 2
6
Ch2. Linear Time-Invariant Systems Convolution Sum
y[n]
k
x[k ]h[n k ]
——Convolution Sum
yn xn hn
x[n]
h[n]
yn xn hn
the unit impulse response h[n] can fully characterize a LTI system.
若：
x(n)：n1 n n2，
则y(n)： n1 n3 n n2 n4
例如：
x(n)： 0 n 3 h(n)： 0 n 4 y(n)： 0 n 7
4个元素 5个元素 8 个元素
16
Ch2. Linear Time-Invariant Systems 2.2 Continuous-Time LTI: Convolution Integral
x[k ]h[1 k ]
10
x[0]h[1] x[1]h[ 2] 6
y[1]
k
x[0]h[1] x[1]h[0] x[2]h[ 1] 10
Example 2.2
1 x[n] 2
Ch2. Linear Time-Invariant Systems
信号与系统目录(Signal and system directory)
信号与系统目录（Signal and system directory）Chapter 1 signals and systems1.1 INTRODUCTION1.2 signalContinuous signals and discrete signalsTwo. Periodic signals and aperiodic signalsThree, real signal and complex signalFour. Energy signal and power signalThe basic operation of 1.3 signalAddition and multiplicationTwo, inversion and TranslationThree, scale transformation (abscissa expansion)1.4 step function and impulse functionFirst, step function and impulse functionTwo. Definition of generalized function of impulse functionThree. The derivative and integral of the impulse functionFour. Properties of the impulse functionDescription of 1.5 systemFirst, the mathematical model of the systemTwo. The block diagram of the systemCharacteristics and analysis methods of 1.6 systemLinearTwo, time invarianceThree, causalityFour, stabilityOverview of five and LTI system analysis methodsExercise 1.32The second chapter is the time domain analysis of continuous systemsThe response of 2.1LTI continuous systemFirst, the classical solution of differential equationTwo, about 0- and 0+ valuesThree, zero input responseFour, zero state responseFive, full response2.2 impulse response and step responseImpulse responseTwo, step response2.3 convolution integralConvolution integralTwo. The convolution diagramThe properties of 2.4 convolution integralAlgebraic operations of convolutionTwo. Convolution of function and impulse function Three. Differential and integral of convolutionFour. Correlation functionExercise 2.34The third chapter is the time domain analysis of discretesystemsThe response of 3.1LTI discrete systemsDifference and difference equationsTwo. Classical solutions of difference equationsThree, zero input responseFour, zero state response3.2 unit sequence and unit sequence responseUnit sequence and unit step sequenceTwo, unit sequence response and step response3.3 convolution sumConvolution sumTwo. The diagram of convolution sumThree. The nature of convolution sum3.4 deconvolutionExercise 3.27The fourth chapter is Fourier transform and frequency domainanalysis of the systemThe 4.1 signal is decomposed into orthogonal functions Orthogonal function setTwo. The signal is decomposed into orthogonal functions 4.2 Fourier seriesDecomposition of periodic signalsTwo, Fourier series of odd even functionThree. Exponential form of Fu Liye seriesThe spectrum of 4.3 period signalFrequency spectrum of periodic signalTwo, the spectrum of periodic matrix pulseThree. The power of periodic signal4.4 the spectrum of aperiodic signalsFirst, Fu Liye transformTwo. Fourier transform of singular functionsProperties of 4.5 Fourier transformLinearTwo, parityThree, symmetryFour, scale transformationFive, time shift characteristicsSix, frequency shift characteristicsSeven. Convolution theoremEight, time domain differential and integral Nine, frequency domain differential and integral Ten. Correlation theorem4.6 energy spectrum and power spectrumEnergy spectrumTwo. Power spectrumFourier transform of 4.7 periodic signals Fourier transform of sine and cosine functionsTwo. Fourier transform of general periodic functionsThree 、 Fu Liye coefficient and Fu Liye transformFrequency domain analysis of 4.8 LTI systemFrequency responseTwo. Distortionless transmissionThree. The response of ideal low-pass filter4.9 sampling theoremSampling of signalsTwo. Time domain sampling theoremThree. Sampling theorem in frequency domainFourier analysis of 4.10 sequencesDiscrete Fourier series DFS of periodic sequencesTwo. Discrete time Fourier transform of non periodic sequences DTFT4.11 discrete Fu Liye and its propertiesDiscrete Fourier transform (DFT)Two. The properties of discrete Fourier transformExercise 4.60The fifth chapter is the S domain analysis of continuous systems 5.1 Laplasse transformFirst, from Fu Liye transform to Laplasse transformTwo. Convergence domainThree, (Dan Bian) Laplasse transformThe properties of 5.2 Laplasse transformLinearTwo, scale transformationThree, time shift characteristicsFour, complex translation characteristicsFive, time domain differential characteristicsSix, time domain integral characteristicsSeven. Convolution theoremEight, s domain differential and integralNine, initial value theorem and terminal value theorem5.3 Laplasse inverse transformationFirst, look-up table methodTwo, partial fraction expansion method5.4 complex frequency domain analysisFirst, the transformation solution of differential equation Two. System functionThree. The s block diagram of the systemFour 、 s domain model of circuitFive, Laplasse transform and Fu Liye transform5.5 bilateral Laplasse transformExercise 5.50The sixth chapter is the Z domain analysis of discrete systems 6.1 Z transformFirst, transform from Laplasse transform to Z transformTwo, z transformThree. Convergence domainProperties of 6.2 Z transformLinearTwo. Displacement characteristicsThree, Z domain scale transformFour. Convolution theoremFive, Z domain differentiationSix, Z domain integralSeven, K domain inversionEight, part sumNine, initial value theorem and terminal value theorem 6.3 inverse Z transformFirst, power series expansion methodTwo, partial fraction expansion method6.4 Z domain analysisThe Z domain solution of difference equationTwo. System functionThree. The Z block diagram of the systemFour 、 the relation between s domain and Z domainFive. Seeking the frequency response of discrete system by means of DTFTExercise 6.50The seventh chapter system function7.1 system functions and system characteristicsFirst, zeros and poles of the system functionTwo. System function and time domain responseThree. System function and frequency domain responseCausality and stability of 7.2 systemsFirst, the causality of the systemTwo, the stability of the system7.3 information flow graphSignal flow graphTwo, Mason formulaStructure of 7.4 systemFirst, direct implementationTwo. Implementation of cascade and parallel connectionExercise 7.39The eighth chapter is the analysis of the state variables of the system8.1 state variables and state equationsConcepts of state and state variablesTwo. State equation and output equationEstablishment of state equation for 8.2 continuous systemFirst, the equation is directly established by the circuit diagramTwo. The equation of state is established by the input-output equationEstablishment and Simulation of state equations for 8.3discrete systemsFirst, the equation of state is established by the input-output equationTwo. The system simulation is made by the state equationSolution of state equation of 8.4 continuous systemFirst, the Laplasse transform method is used to solve the equation of stateTwo, the system function matrix H (z) and the stability of the systemThree. Solving state equation by time domain methodSolution of state equation for 8.5 discrete systemsFirst, the time domain method is used to solve the state equations of discrete systemsTwo. Solving the state equation of discrete system by Z transformThree, the system function matrix H (z) and the stability of the systemControllability and observability of 8.6 systemsFirst, the linear transformation of state vectorTwo, the controllability and observability of the systemExercise 8.32Appendix a convolution integral tableAppendix two convolution and tableAppendix three Fourier coefficients table of commonly used periodic signalsAppendix four Fourier transform tables of commonly used signalsAppendix five Laplasse inverse exchange tableAppendix six sequence of the Z transform table。
tpo45三篇托福阅读TOEFL原文译文题目答案译文背景知识
tpo45三篇托福阅读TOEFL原文译文题目答案译文背景知识阅读-1 (2)原文 (2)译文 (5)题目 (7)答案 (15)背景知识 (16)阅读-2 (16)原文 (16)译文 (19)题目 (23)答案 (30)背景知识 (31)阅读-3 (32)原文 (32)译文 (35)题目 (37)答案 (45)背景知识 (45)阅读-1原文The Beringia Landscape①During the peak of the last ice age,northeast Asia(Siberia)and Alaska were connected by a broad land mass called the Bering Land Bridge.This land bridge existed because so much of Earth’s water was frozen in the great ice sheets that sea levels were over100meters lower than they are today.Between25,000and10,000years ago,Siberia,the Bering Land Bridge,and Alaska shared many environmental characteristics.These included a common mammalian fauna of large mammals,a common flora composed of broad grasslands as well as wind-swept dunes and tundra,and a common climate with cold,dry winters and somewhat warmer summers.The recognition that many aspects of the modern flora and fauna were present on both sides of the Bering Sea as remnants of the ice-age landscape led to this region being named Beringia.②It is through Beringia that small groups of large mammal hunters, slowly expanding their hunting territories,eventually colonized North and South America.On this archaeologists generally agree,but that is where the agreement stops.One broad area of disagreement inexplaining the peopling of the Americas is the domain of paleoecologists,but it is critical to understanding human history:what was Beringia like?③The Beringian landscape was very different from what it is today. Broad,windswept valleys;glaciated mountains;sparse vegetation;and less moisture created a rather forbidding land mass.This land mass supported herds of now-extinct species of mammoth,bison,and horse and somewhat modern versions of caribou,musk ox,elk,and saiga antelope.These grazers supported in turn a number of impressive carnivores,including the giant short-faced bear,the saber-tooth cat,and a large species of lion.④The presence of mammal species that require grassland vegetation has led Arctic biologist Dale Guthrie to argue that while cold and dry, there must have been broad areas of dense vegetation to support herds of mammoth,horse,and bison.Further,nearly all of the ice-age fauna had teeth that indicate an adaptation to grasses and sedges;they could not have been supported by a modern flora of mosses and lichens. Guthrie has also demonstrated that the landscape must have been subject to intense and continuous winds,especially in winter.He makes this argument based on the anatomy of horse and bison,which do not have the ability to search for food through deep snow cover.They needlandscapes with strong winds that remove the winter snows,exposing the dry grasses beneath.Guthrie applied the term“mammoth steppe"to characterize this landscape.⑤In contrast,Paul Colinvaux has offered a counterargument based on the analysis of pollen in lake sediments dating to the last ice age.He found that the amount of pollen recovered in these sediments is so low that the Beringian landscape during the peak of the last glaciation was more likely to have been what he termed a"polar desert,"with little or only sparse vegetation,in no way was it possible that this region could have supported large herds of mammals and thus,human hunters. Guthrie has argued against this view by pointing out that radiocarbon analysis of mammoth,horse,and bison bones from Beringian deposits revealed that the bones date to the period of most intense glaciation.⑥The argument seemed to be at a standstill until a number of recent studies resulted in a spectacular suite of new finds.The first was the discovery of a1,000-square-kilometer preserved patch of Beringian vegetation dating to just over17,000years ago—the peak of the last ice age.The plants were preserved under a thick ash fall from a volcanic eruption.Investigations of the plants found grasses,sedges,mosses,and many other varieties in a nearly continuous cover,as was predicted by Guthrie.But this vegetation had a thin root mat with no soil formation,demonstrating that there was little long-term stability in plant cover,a finding supporting some of the arguments of Colinvaux.A mixture of continuous but thin vegetation supporting herds of large mammals is one that seems plausible and realistic with the available data.译文洞察白令地貌①在上一次冰期的高峰，东北亚地区（西伯利亚）和阿拉斯加曾由一片广阔的陆地相连，这片土地被叫做白令陆桥。
专业英语词汇(信号与系统)
《信号与系统》专业术语中英文对照表第 1 章绪论信号（signal）系统（system）电压（voltage）电流（current）信息（information）电路（circuit）网络（network）确定性信号（determinate signal）随机信号（random signal）一维信号（one–dimensional signal）多维信号（multi–dimensional signal）连续时间信号（continuous time signal）离散时间信号（discrete time signal）取样信号（sampling signal）数字信号（digital signal）周期信号（periodic signal）非周期信号（nonperiodic（aperiodic）signal）能量（energy）功率（power）能量信号（energy signal）功率信号（power signal）平均功率（average power）平均能量（average energy）指数信号（exponential signal）时间常数（time constant）正弦信号（sine signal）余弦信号（cosine signal）振幅（amplitude）角频率（angular frequency）初相位（initial phase）周期（period）频率（frequency）欧拉公式（Euler’s formula）复指数信号（complex exponential signal）复频率（complex frequency）实部（real part）虚部（imaginary part）抽样函数Sa(t)（sampling（Sa）function）偶函数（even function）奇异函数（singularity function）- 奇异信号（singularity signal）单位斜变信号（unit ramp signal）斜率（slope）单位阶跃信号（unit step signal）符号函数（signum function）单位冲激信号（unit impulse signal）广义函数（generalized function）取样特性（sampling property）冲激偶信号（impulse doublet signal）奇函数（odd function）偶分量（even component）奇分量（odd component）正交函数（orthogonal function）正交函数集（set of orthogonal function）数学模型（mathematics model）电压源（voltage source）基尔霍夫电压定律（Kirchhoff’s voltage law（KVL））电流源（current source）连续时间系统（continuous time system）离散时间系统（discrete time system）微分方程（differential function）差分方程（difference function）线性系统（linear system）非线性系统（nonlinear system）时变系统（time–varying system）时不变系统（time–invariant system）集总参数系统（lumped–parameter system）分布参数系统（distributed–parameter system）偏微分方程（partial differential function）因果系统（causal system）非因果系统（noncausal system）因果信号（causal signal）叠加性（superposition property）均匀性（homogeneity）积分（integral）输入–输出描述法（input–output analysis）状态变量描述法（state variable analysis）单输入单输出系统（single–input and single–output system）状态方程（state equation）输出方程（output equation）多输入多输出系统（multi–input and multi–output system）时域分析法（time domain method）变换域分析法（transform domain method）卷积（convolution）傅里叶变换（Fourier transform）拉普拉斯变换（Laplace transform）- 第 2 章连续时间系统的时域分析齐次解（homogeneous solution）特解（particular solution）特征方程（characteristic function）特征根（characteristic root）固有（自由）解（natural solution）强迫解（forced solution）起始条件（original condition）初始条件（initial condition）自由响应（natural response）强迫响应（forced response）零输入响应（zero-input response）零状态响应（zero-state response）冲激响应（impulse response）阶跃响应（step response）卷积积分（convolution integral）交换律（exchange law）分配律（distribute law）结合律（combine law）第3 章傅里叶变换频谱（frequency spectrum）频域（frequency domain）三角形式的傅里叶级数（trigonomitric Fourier series）指数形式的傅里叶级数（exponential Fourier series）傅里叶系数（Fourier coefficient）直流分量（direct composition）基波分量（fundamental composition）n 次谐波分量（n th harmonic component）复振幅（complex amplitude）频谱图（spectrum plot（diagram））幅度谱（amplitude spectrum）相位谱（phase spectrum）包络（envelop）离散性（discrete property）谐波性（harmonic property）收敛性（convergence property）奇谐函数（odd harmonic function）吉伯斯现象（Gibbs phenomenon）周期矩形脉冲信号（periodic rectangular pulse signal）周期锯齿脉冲信号（periodic sawtooth pulse signal）周期三角脉冲信号（periodic triangular pulse signal）- 周期半波余弦信号（periodic half–cosine signal）周期全波余弦信号（periodic full–cosine signal）傅里叶逆变换（inverse Fourier transform）频谱密度函数（spectrum density function）单边指数信号（single–sided exponential signal）双边指数信号（two–sided exponential signal）对称矩形脉冲信号（symmetry rectangular pulse signal）线性（linearity）对称性（symmetry）对偶性（duality）位移特性（shifting）时移特性（time–shifting）频移特性（frequency–shifting）调制定理（modulation theorem）调制（modulation）解调（demodulation）变频（frequency conversion）尺度变换特性（scaling）微分与积分特性（differentiation and integration）时域微分特性（differentiation in the time domain）时域积分特性（integration in the time domain）频域微分特性（differentiation in the frequency domain）频域积分特性（integration in the frequency domain）卷积定理（convolution theorem）时域卷积定理（convolution theorem in the time domain）频域卷积定理（convolution theorem in the frequency domain）取样信号（sampling signal）矩形脉冲取样（rectangular pulse sampling）自然取样（nature sampling）冲激取样（impulse sampling）理想取样（ideal sampling）取样定理（sampling theorem）调制信号（modulation signal）载波信号（carrier signal）已调制信号（modulated signal）模拟调制（analog modulation）数字调制（digital modulation）连续波调制（continuous wave modulation）脉冲调制（pulse modulation）幅度调制（amplitude modulation）频率调制（frequency modulation）相位调制（phase modulation）角度调制（angle modulation）频分多路复用（frequency–division multiplex（FDM））时分多路复用（time–division multiplex（TDM））相干（同步）解调（synchronous detection）- 本地载波（local carrier）系统函数（system function）网络函数（network function）频响特性（frequency response）幅频特性（amplitude frequency response）相频特性（phase frequency response）无失真传输（distortionless transmission）理想低通滤波器（ideal low–pass filter）截止频率（cutoff frequency）正弦积分（sine integral）上升时间（rise time）窗函数（window function）理想带通滤波器（ideal band–pass filter）第 4 章拉普拉斯变换代数方程（algebraic equation）双边拉普拉斯变换（two-sided Laplace transform）双边拉普拉斯逆变换（inverse two-sided Laplace transform）单边拉普拉斯变换（single-sided Laplace transform）拉普拉斯逆变换（inverse Laplace transform）收敛域（region of convergence（ROC））延时特性（time delay）s 域平移特性（shifting in the s-domain）s 域微分特性（differentiation in the s-domain）s 域积分特性（integration in the s-domain）初值定理（initial-value theorem）终值定理（expiration-value）复频域卷积定理（convolution theorem in the complex frequency domain）部分分式展开法（partial fraction expansion）留数法（residue method）第 5 章策动点函数（driving function）转移函数（transfer function）极点（pole）零点（zero）零极点图（zero-pole plot）暂态响应（transient response）稳态响应（stable response）稳定系统（stable system）一阶系统（first order system）高通滤波网络（high-low filter）低通滤波网络（low-pass filter）- 二阶系统（second system）最小相移系统（minimum-phase system）维纳滤波器（Winner filter）卡尔曼滤波器（Kalman filter）低通（low-pass）高通（high-pass）带通（band-pass）带阻（band-stop）有源（active）无源（passive）模拟（analog）数字（digital）通带（pass-band）阻带（stop-band）佩利－维纳准则（Paley-Winner criterion）最佳逼近（optimum approximation）过渡带（transition-band）通带公差带（tolerance band）巴特沃兹滤波器（Butterworth filter）切比雪夫滤波器（Chebyshew filter）方框图（block diagram）信号流图（signal flow graph）节点（node）支路（branch）输入节点（source node）输出节点（sink node）混合节点（mix node）通路（path）开通路（open path）闭通路（close path）环路（loop）自环路（self-loop）环路增益（loop gain）不接触环路（disconnect loop）前向通路（forward path）前向通路增益（forward path gain）梅森公式（Mason formula）劳斯准则（Routh criterion）第 6 章数字系统（digital system）数字信号处理（digital signal processing）差分方程（difference equation）单位样值响应（unit sample response）卷积和（convolution sum）- Z 变换（Z transform）序列（sequence）样值（sample）单位样值信号（unit sample signal）单位阶跃序列（unit step sequence）矩形序列(rectangular sequence)单边实指数序列（single sided real exponential sequence）单边正弦序列（single sided exponential sequence）斜边序列（ramp sequence）复指数序列（complex exponential sequence）线性时不变离散系统（linear time-invariant discrete-time system）常系数线性差分方程（linear constant-coefficient difference equation）后向差分方程（backward difference equation）前向差分方程（forward difference equation）海诺塔（Tower of Hanoi）菲波纳西（Fibonacci）冲激函数串（impulse train）第7 章数字滤波器（digital filter）单边Z 变换（single-sided Z transform）双边Z 变换(two-sided (bilateral) Z transform)幂级数（power series）收敛（convergence）有界序列（limitary-amplitude sequence）正项级数（positive series）有限长序列（limitary-duration sequence）右边序列（right-sided sequence）左边序列（left-sided sequence）双边序列（two-sided sequence）Z 逆变换（inverse Z transform）围线积分法（contour integral method）幂级数展开法（power series expansion）z 域微分（differentiation in the z-domain）序列指数加权（multiplication by an exponential sequence）z 域卷积定理（z-domain convolution theorem）帕斯瓦尔定理（Parseval theorem）传输函数（transfer function）序列的傅里叶变换（discrete-time Fourier transform：DTFT）序列的傅里叶逆变换（inverse discrete-time Fourier transform：IDTFT）幅度响应（magnitude response）相位响应（phase response）量化（quantization）编码（coding）模数变换（A/D 变换：analog-to-digital conversion）- 数模变换（D/A 变换：digital-to- analog conversion）第8 章端口分析法（port analysis）状态变量（state variable）无记忆系统（memoryless system）有记忆系统（memory system）矢量矩阵（vector-matrix ）常量矩阵（constant matrix ）输入矢量（input vector）输出矢量（output vector）直接法（direct method）间接法（indirect method）状态转移矩阵（state transition matrix）系统函数矩阵（system function matrix）冲激响应矩阵（impulse response matrix）朱里准则（July criterion）。
Prony算法入门
(2.2.3) by fitting a sum of complex damped sinusoids to evenly spaced sample (in time)
values of the output:
^
L
∑ y(t) = Aie(σit) cos(2πfit + φi ) .
i =1
In (2.2.6), we have utilized the following notations:
2.2 Original Prony Analysis To derive the mathematical formulation for the original Prony analysis, let us
consider a Pulsed Corona Reactor (PCR) as a linear time-invariant (LTI) dynamic system as shown in Figure 2.2.1.
(2.2.6)
Ai: Amplitude of component i, σ i : Damping coefficient of component i, φi : Phase of component i,
fi : Frequency of component i, L: Total number of damped exponential components,
The Prony analysis (PA) is known to behave poorly when a signal is embedded in noise (Marple 1987). It yields parameter estimates with a large bias due to its sensitivity to measurement noise. It does not make a separate estimate of the noise. It also fits exponentials to any additive noise present in the signal. When PA is applied to a signal
“信号与系统”中系统稳定性分析
“信号与系统”中系统稳定性分析巩亚楠 魏德旺 刘俊良 李淑晴 吕海燕*(临沂大学 山东临沂 276000)摘要：“信号与系统”是电子信息类本科阶段的专业基础课。
在学习的过程中，很多同学只是记住知识点，不明白它们之间的逻辑关系，不会灵活运用。
该文旨在利用思维导图的方式对系统稳定性分析方法进行总结，描述了连续时间系统和离散时间系统的稳定性，对每个系统提出了两种分析方法，即时域分析法和变换域分析法，对两种方法的具体分析过程做出了详细的说明，并对系统稳定性给出了4种判别方法。
借助思维导图，帮助学生更好地理解知识，充分调动学生学习的积极性。
关键词：信号与系统 思维导图 系统稳定性分析 连续时间系统 离散时间系统中图分类号：G64文献标识码：A 文章编号：1672-3791(2023)18-0078-04 Analysis of the System Stability in "Signals and Systems"GONG Yanan WEI Dewang LIU Junliang LI Shuqing LYU Haiyan*(Linyi University, Linyi, Shandong Province, 276000 China) Abstract:"Signals and systems" i s a professional basic course of the undergraduate level of electronic information. In the process of learning, many students just remember knowledge points, but they don't understand the logic rela‐tionship among them and cannot use them freely. This paper aims to summarize the analytical method of the system stability by mind mapping, describes the stability of the continuous-time system and the discrete-time system, puts forward two analytical methods for each system, namely the time-domain analysis method and the transform-domain analysis method, explains in detail the specific analytical process of the two methods, and also presents four discriminant methods for the system stability. With the help of mind mapping, students can better comprehend knowledge and fully mobilize their enthusiasm for learning.Key Words: Signals and Systems; Mind mapping; System stability analysis; Continuous-time system; Discrete-time system1 “信号与系统”课程地位“信号与系统”作为信息、电子、自控、通信等专业的专业基础课，是为后续数字信号处理、数字图像处理、通信原理、自动控制等课程的学习打下基础，“信号与系统分析”被认为是一门理解困难、计算繁杂、偏理论模型的课程。
信号与系统翻译
This school gave me the first impression is that there are a lot of trees and flowers, the campus is very large, very beautiful.I consider living here and learning is a wonderful thing!这本知名且被高度评价的书本的第二版，可以用来作为一个或两个学期的本科信号与线性系统理论和应用的基础课程。
它的内容包括信号和系统的基本概念，线性时不变（LTI）系统，连续时间和离散时间信号的傅立叶表示，连续时间和离散时间傅里叶变换和时域和频域分析方法。
作者通过在过滤，采样，通信，反馈中使用大量的实例来强调理论的应用。
并行讨论了连续时间和离散时间的频域方法，让读者能够运用横跨两个领域的见解和直觉。
它也通过对时域和频域的相似性和差异性的比较来帮助读者对材料有更深入的理解。
本书还包括对通信系统和控制理论的介绍章节。
学习本书假定你有了解微积分以及承受复杂的数字和基本微分方程运算的能力。
因为它的完整性和适当的进度，本书被高度推荐给学生和那些有兴趣自学的人。
The second edition of this well-known and highly regarded text can be used as the basis for a one- or two-semester undergraduate course in signals and linear systems theory and applications. Topics include basic signals and systems concepts, linear time-invariant (LTI) systems, Fourier representations of continuous-time and discrete-time signals, the CT and DT Fourier transforms, and time- and frequency-domain analysis methods. The author emphasizes applications of the theory through numerous examples in filtering, sampling, communications, and feedback. The parallel development of continuous-time and discrete-time frequency domain methods allows the reader to apply insights and intuition across the two domains. It also facilitates a deeper understanding of the material by bringing into focus the similarities and differences between the two domains. The text also includes introductory chapters on communication systems and control theory. This book assumes that you have a background in calculus as well as exposure to complex numbers and elementary differential equations. Because of its thoroughness and unhurried pace, this text is highly recommended for students and those interested in self-study.。
数字信号处理英语词汇
AAbsolutely integrable绝对可积Absolutely integrable impulse response绝对可积冲激响应Absolutely summable绝对可和Absolutely summable impulse response绝对可和冲激响应Accumulator累加器Acoustic 声学Adder加法器Additivity property可加性Aliasing混叠现象All-pass systems全通系统AM (Amplitude modulation )幅度调制Amplifier放大器Amplitude modulation (AM)幅度调制Amplitude-scaling factor幅度放大因子Analog-to-digital (A-to-D) converter模数转换器Analysis equation分析公式（方程）Angel (phase) of complex number复数的角度（相位）Angle criterion角判据Angle modulation角度调制Anticausality反因果Aperiodic非周期Aperiodic convolution非周期卷积Aperiodic signal非周期信号Asynchronous异步的Audio systems音频（声音）系统Autocorrelation functions自相关函数Automobile suspension system汽车减震系统Averaging system平滑系统BBand-limited带（宽）限的Band-limited input signals带限输入信号Band-limited interpolation带限内插Bandpass filters带通滤波器Bandpass signal带通信号Bandpass-sampling techniques带通采样技术Bandwidth带宽Bartlett (triangular) window巴特利特（三角形）窗Bilateral Laplace transform双边拉普拉斯变换Bilinear双线性的Bilinear transformation双线性变换Bit（二进制）位，比特Block diagrams方框图Bode plots波特图Bounded有界限的Break frequency折转频率Butterworth filters巴特沃斯滤波器C“Chirp” transform algorithm“鸟声”变换算法Capacitor电容器Carrier载波Carrier frequency载波频率Carrier signal载波信号Cartesian (rectangular) form 直角坐标形式Cascade (series) interconnection串联，级联Cascade-form串联形式Causal LTI system因果的线性时不变系统Channel信道，频道Channel equalization信道均衡Chopper amplifier斩波器放大器Closed-loop闭环Closed-loop poles闭环极点Closed-loop system闭环系统Closed-loop system function闭环系统函数Coefficient multiplier系数乘法器Coefficients系数Communications systems通信系统Commutative property交换性（交换律）Compensation for nonideal elements非理想元件的补偿Complex conjugate复数共轭Complex exponential carrier复指数载波Complex exponential signals复指数信号Complex exponential(s)复指数Complex numbers 复数Conditionally stable systems条件稳定系统Conjugate symmetry共轭对称Conjugation property共轭性质Continuous-time delay连续时间延迟Continuous-time filter连续时间滤波器Continuous-time Fourier series连续时间傅立叶级数Continuous-time Fourier transform连续时间傅立叶变换Continuous-time signals连续时间信号Continuous-time systems连续时间系统Continuous-to-discrete-time conversion连续时间到离散时间转换Convergence 收敛Convolution卷积Convolution integral卷积积分Convolution property卷积性质Convolution sum卷积和Correlation function相关函数Critically damped systems临界阻尼系统Crosss-correlation functions互相关函数Cutoff frequencies截至频率DDamped sinusoids阻尼正弦振荡Damping ratio阻尼系数Dc offset直流偏移Dc sequence直流序列Deadbeat feedback systems临界阻尼反馈系统Decibels (dB) 分贝Decimation抽取Decimation and interpolation抽取和内插Degenerative (negative) feedback负反馈Delay延迟Delay time延迟时间Demodulation解调Difference equations差分方程Differencing property差分性质Differential equations微分方程Differentiating filters微分滤波器Differentiation property微分性质Differentiator微分器Digital-to-analog (D-to-A) converter数模转换器Direct Form I realization直接I型实现Direct form II realization直接II型实现Direct-form直接型Dirichlet conditions狄里赫利条件Dirichlet, P.L.狄里赫利Discontinuities间断点，不连续Discrete-time filters 离散时间滤波器Discrete-time Fourier series离散时间傅立叶级数Discrete-time Fourier series pair离散时间傅立叶级数对Discrete-time Fourier transform （DFT）离散时间傅立叶变换Discrete-time LTI filters离散时间线性时不变滤波器Discrete-time modulation离散时间调制Discrete-time nonrecursive filters离散时间非递归滤波器Discrete-time signals离散时间信号Discrete-time systems离散时间系统Discrete-time to continuous-time conversion离散时间到连续时间转换Dispersion弥撒（现象）Distortion扭曲，失真Distribution theory（property）分配律Dominant time constant主时间常数Double-sideband modulation (DSB)双边带调制Downsampling减采样Duality对偶性EEcho回波Eigenfunctions特征函数Eigenvalue特征值Elliptic filters椭圆滤波器Encirclement property围线性质End points终点Energy of signals信号的能量Energy-density spectrum能量密度谱Envelope detector包络检波器Envelope function包络函数Equalization均衡化Equalizer circuits均衡器电路Equation for closed-loop poles闭环极点方程Euler, L.欧拉Euler’s relation欧拉关系（公式）Even signals偶信号Exponential signals指数信号Exponentials指数FFast Fourier transform (FFT)快速傅立叶变换Feedback反馈Feedback interconnection反馈联结Feedback path反馈路径Filter(s)滤波器Final-value theorem终值定理Finite impulse response (FIR)有限长脉冲响应Finite impulse response (FIR) filters有限长脉冲响应滤波器Finite sum formula有限项和公式Finite-duration signals有限长信号First difference一阶差分First harmonic components基波分量（一次谐波分量）First-order continuous-time systems一阶连续时间系统First-order discrete-time systems一阶离散时间系统First-order recursive discrete-time filters一阶递归离散时间滤波器First-order systems一阶系统Forced response受迫响应Forward path正向通路Fourier series傅立叶级数Fourier transform傅立叶变换Fourier transform pairs傅立叶变换对Fourier, Jean Baptiste Joseph傅立叶（法国数学家，物理学家）Frequency response频率响应Frequency response of LTI systems线性时不变系统的频率响应Frequency scaling of continuous-time Fourier transform 连续时间傅立叶变化的频率尺度（变换性质）Frequency shift keying (FSK)频移键控Frequency shifting property频移性质Frequency-division multiplexing (FDM)频分多路复用Frequency-domain characterization频域特征Frequency-selective filter频率选择滤波器Frequency-shaping filters频率成型滤波器Fundamental components基波分量Fundamental frequency基波频率Fundamental period基波周期GGain增益Gain and phase margin增益和相位裕度General complex exponentials一般复指数信号Generalized functions广义函数Gibbs phenomenon吉伯斯现象Group delay群延迟HHalf-sample delay半采样间隔时延Hanning window汉宁窗Harmonic analyzer谐波分析议Harmonic components谐波分量Harmonically related谐波关系Heat propagation and diffusion热传播和扩散现象Higher order holds高阶保持Highpass filter高通滤波器Highpass-to-lowpass transformations高通到低通变换Hilbert transform希尔波特滤波器Homogeneity (scaling) property齐次性（比例性）IIdeal理想的Ideal bandstop characteristic理想带阻特征Ideal frequency-selective filter理想频率选择滤波器Idealization理想化Identity system恒等系统Imaginary part虚部Impulse response 冲激响应Impulse train冲激串Incrementally linear systems增量线性系统Independent variable独立变量Infinite impulse response (IIR)无限长脉冲响应Infinite impulse response (IIR) filters无限长脉冲响应滤波器Infinite sum formula无限项和公式Infinite taylor series无限项泰勒级数Initial-value theorem初值定理Inpulse-train sampling冲激串采样Instantaneous瞬时的Instantaneous frequency瞬时频率Integration in time-domain时域积分Integration property积分性质Integrator积分器Interconnection互联Intermediate-frequency (IF) stage中频级Intersymbol interference (ISI)码间干扰Inverse Fourier transform傅立叶反变换Inverse Laplace transform拉普拉斯反变换Inverse LTI system逆线性时不变系统Inverse system design逆系统设计Inverse z-transform z反变换Inverted pendulum倒立摆Invertibility of LTI systems线性时不变系统的可逆性Invertible systems逆系统LLag network滞后网络Lagrange, J.L.拉格朗日（法国数学家，力学家）Laplace transform拉普拉斯变换Laplace, P.S. de拉普拉斯（法国天文学家，数学家）lead network超前网络left-half plane左半平面left-sided signal左边信号Linear线性Linear constant-coefficient difference线性常系数差分方程equationsLinear constant-coefficient differential线性常系数微分方程equationsLinear feedback systems线性反馈系统Linear interpolation线性插值Linearity线性性Log magnitude-phase diagram对数幅－相图Log-magnitude plots对数模图Lossless coding无损失码Lowpass filters低通滤波器Lowpass-to-highpass transformation低通到高通的转换LTI system response线性时不变系统响应LTI systems analysis线性时不变系统分析MMagnitude and phase幅度和相位Matched filter匹配滤波器Measuring devices测量仪器Memory记忆Memoryless systems无记忆系统Modulating signal调制信号Modulation调制Modulation index调制指数Modulation property调制性质Moving-average filters移动平均滤波器Multiplexing多路技术Multiplication property相乘性质Multiplicities多样性NNarrowband窄带Narrowband frequency modulation窄带频率调制Natural frequency自然响应频率Natural response自然响应Negative (degenerative) feedback负反馈Nonanticipatibe system不超前系统Noncausal averaging system非因果平滑系统Nonideal非理想的Nonideal filters非理想滤波器Nonmalized functions归一化函数Nonrecursive非递归Nonrecursive filters非递归滤波器Nonrecursive linear constant-coefficient非递归线性常系数差分方程difference equationsNyquist frequency奈奎斯特频率Nyquist rate奈奎斯特率Nyquist stability criterion奈奎斯特稳定性判据OOdd harmonic 奇次谐波Odd signal奇信号Open-loop开环Open-loop frequency response开环频率响应Open-loop system开环系统Operational amplifier运算放大器Orthogonal functions正交函数Orthogonal signals正交信号Oscilloscope示波器Overdamped system过阻尼系统Oversampling过采样Overshoot超量PParallel interconnection并联Parallel-form block diagrams并联型框图Parity check奇偶校验检查Parseval’s relation帕斯伐尔关系（定理）Partial-fraction expansion部分分式展开Particular and homogeneous solution特解和齐次解Passband通频带Passband edge通带边缘Passband frequency通带频率Passband ripple通带起伏（或波纹）Pendulum钟摆Percent modulation调制百分数Periodic周期的Periodic complex exponentials周期复指数Periodic convolution周期卷积Periodic signals周期信号Periodic square wave周期方波Periodic square-wave modulating signal周期方波调制信号Periodic train of impulses周期冲激串Phase (angle) of complex number复数相位（角度）Phase lag相位滞后Phase lead相位超前Phase margin相位裕度Phase shift相移Phase-reversal相位倒置Phase modulation相位调制Plant工厂Polar form极坐标形式Poles极点Pole-zero plot(s)零极点图Polynomials 多项式Positive (regenerative) feedback正（再生）反馈Power of signals信号功率Power-series expansion method幂级数展开的方法Principal-phase function主值相位函数Proportional (P) control比例控制Proportional feedback system比例反馈系统Proportional-plus-derivative比例加积分Proportional-plus-derivative feedback比例加积分反馈Proportional-plus-integral-plus-different比例－积分－微分控制ial (PID) controlPulse-amplitude modulation脉冲幅度调制Pulse-code modulation脉冲编码调制Pulse-train carrier冲激串载波QQuadrature distortion正交失真Quadrature multiplexing正交多路复用Quality of circuit电路品质（因数）RRaised consine frequency response升余弦频率响应Rational frequency responses有理型频率响应Rational transform有理变换RC highpass filter RC 高阶滤波器RC lowpass filter RC 低阶滤波器Real实数Real exponential signals实指数信号Real part实部Rectangular (Cartesian) form 直角（卡笛儿）坐标形式Rectangular pulse矩形脉冲Rectangular pulse signal矩形脉冲信号Rectangular window矩形窗口Recursive (infinite impulse response)递归（无时限脉冲响应）滤波器filtersRecursive linear constant-coefficient 递归的线性常系数差分方程difference equationsRegenerative (positive) feedback再生（正）反馈Region of comvergence收敛域right-sided signal右边信号Rise time上升时间Root-locus analysis根轨迹分析（方法）Running sum动求和SS domain S域Sampled-data feedback systems采样数据反馈系统Sampled-data systems采样数据系统Sampling采样Sampling frequency采样频率Sampling function采样函数Sampling oscilloscope采样示波器Sampling period采样周期Sampling theorem采样定理Scaling (homogeneity) property比例性（齐次性）性质Scaling in z domain z域尺度变换Scrambler扰频器Second harmonic components二次谐波分量Second-order二阶Second-order continuous-time system二阶连续时间系统Second-order discrete-time system二阶离散时间系统Second-order systems二阶系统sequence序列Series (cascade) interconnection级联（串联）Sifting property筛选性质Sinc functions sinc函数Single-sideband单边带Single-sideband sinusoidal amplitude单边带正弦幅度调制modulationSingularity functions奇异函数Sinusoidal正弦（信号）Sinusoidal amplitude modulation正弦幅度调制Sinusoidal carrier正弦载波Sinusoidal frequency modulation正弦频率调制Sliding滑动Spectral coefficient频谱系数Spectrum频谱Speech scrambler语音加密器S-plane S平面Square wave方波Stability稳定性Stabilization of unstable systems不稳定系统的稳定性（度）Step response阶跃响应Step-invariant transformation阶跃响应不定的变换Stopband阻带Stopband edge阻带边缘Stopband frequency阻带频率Stopband ripple 阻带起伏（或波纹）Stroboscopic effect频闪响应Summer加法器Superposition integral叠加积分Superposition property叠加性质Superposition sum叠加和Suspension system减震系统Symmetric periodic 周期对称Symmetry对称性Synchronous同步的Synthesis equation综合方程System function(s)系统方程TTable of properties 性质列表Taylor series泰勒级数Time时间，时域Time advance property of unilateral单边z变换的时间超前性质z-transformTime constants时间常数Time delay property of unilateral单边z变换的时间延迟性质z-transformTime expansion property时间扩展性质Time invariance时间变量Time reversal property时间反转（反褶）性Time scaling property时间尺度变换性Time shifting property时移性质Time window时间窗口Time-division multiplexing (TDM)时分复用Time-domain时域Time-domain properties时域性质Tracking system (s)跟踪系统Transfer function转移函数transform pairs变换对Transformation变换（变形）Transition band过渡带Transmodulation (transmultiplexing) 交叉调制Triangular (Barlett) window三角型（巴特利特）窗口Trigonometric series三角级数Two-sided signal双边信号Type l feedback system l 型反馈系统UUint impulse response单位冲激响应Uint ramp function单位斜坡函数Undamped natural frequency无阻尼自然相应Undamped system无阻尼系统Underdamped systems欠阻尼系统Undersampling欠采样Unilateral单边的Unilateral Laplace transform单边拉普拉斯变换Unilateral z-transform单边z变换Unit circle单位圆Unit delay单位延迟Unit doublets单位冲激偶Unit impulse单位冲激Unit step functions单位阶跃函数Unit step response 单位阶跃响应Unstable systems不稳定系统Unwrapped phase展开的相位特性Upsampling增采样VVariable变量WWalsh functions沃尔什函数Wave波形Wavelengths波长Weighted average加权平均Wideband宽带Wideband frequency modulation宽带频率调制Windowing加窗zZ domain z域Zero force equalizer置零均衡器Zero-Input response零输入响应Zero-Order hold零阶保持Zeros of Laplace transform拉普拉斯变换的零点Zero-state response零状态响应z-transform z变换z-transform pairs z变换对。
自动控制原理与设计 第5版 英文
自动控制原理与设计第5版英文Automatic Control Principles and Design 5th EditionIntroduction:Automatic control principles and design play a crucial role in various engineering fields, enabling the efficient operation of systems and processes. In this article, we delve into the key concepts and applications of automatic control, as outlined in the 5th edition of the book "Automatic Control Principles and Design."Chapter 1: Introduction to Automatic ControlAutomatic control is the use of control systems to regulate processes or machines without human intervention. It encompasses a wide range of applications, from simple domestic appliances to complex industrial systems. The chapter provides an overview of the basic principles and benefits of automatic control.Chapter 2: Modeling of Dynamic SystemsThe accurate modeling of dynamic systems is essential for effective control design. This chapter explores different techniques for modeling linear and nonlinear systems, including differential equations, transfer functions, and state-space representations. Real-world examples are used to illustrate the modeling process.Chapter 3: Time-Domain Analysis of Control SystemsTime-domain analysis allows us to examine the transient and steady-state responses of control systems. This chapter covers the analysis of first-and second-order systems, as well as higher-order systems. It also introduces the concept of system stability and the influence of system parameters on stability.Chapter 4: Frequency-Domain Analysis of Control SystemsFrequency-domain analysis provides insights into the behavior of control systems in the frequency spectrum. The chapter discusses transfer function analysis, Bode plots, Nyquist plots, and the relationship between the time- and frequency-domain representations of systems. Practical examples are included to enhance understanding.Chapter 5: Control System Design by Root Locus TechniqueThe root locus technique is a graphical method that aids in control system design. This chapter explores the construction of the root locus plot and its use in determining system stability, transient response, and controller design. Design guidelines and examples are presented to illustrate the application of this powerful tool.Chapter 6: Control System Design by Frequency Response TechniqueFrequency response techniques provide an alternative approach to control system design. This chapter discusses the design of compensators and filters using frequency response methods such as gain and phase margins and loop shaping. The advantages and limitations of this design approach are highlighted.Chapter 7: State-Space Analysis and DesignState-space analysis offers a modern and comprehensive framework for control system design. This chapter presents the concepts of state variables, state equations, observability, and controllability. The methods for state feedback control and observer design are also covered, along with their applications.Chapter 8: Digital Control SystemsThe design and implementation of control systems in the digital domain are covered in this chapter. It discusses the advantages of digital control, discretization of continuous-time systems, sampling and quantization, and various digital control algorithms. Practical considerations and implementation issues are addressed.Chapter 9: Introduction to Nonlinear Systems and ControlNonlinear systems present unique challenges in control design. This chapter introduces the basics of nonlinear systems and control techniques. It covers phase-plane analysis, describing functions, feedback linearization, and sliding mode control. Real-world examples demonstrate the application of these methods.Conclusion:The 5th edition of "Automatic Control Principles and Design" provides a comprehensive and up-to-date resource for understanding the principles and design techniques in automatic control. Through the exploration of different chapters, readers gain the necessary knowledge and skills to design effective control systems for a wide range of applications. This book serves as aninvaluable guide for students, researchers, and professionals in the field of automatic control.。
4Signals
Signals&Systems信号与系统SUM:We learned the transform of signals and their application in system analyze,for example in Time domain analysis,the Fourier Transform and Frequency domain analysis,the Laplace Transform and the Complex Domain Analysis,the Z-transform.SUM:我们学习了信号的变换及其在系统分析中的应用，例如时域分析，傅里叶变换和频域分析，拉普拉斯变换和复域分析，z 变换。
1、What is a signal?--signals carry the information we need.In communIcation technology,we call words,images,datas and so on signals.There are continuous signals and discrete signals.什么是信号?——信号携带我们需要的信息。
在通信技术中，我们把文字、图像、数据等称为信号。
有连续信号和离散信号。
Signals are physical quantities that change over time.信号是随时间变化的物理量。
2、A system is any physical set of components that takes a signal and produces a signal.系统是接收信号并产生信号的任何物理组件集。
A system can be classified as linear or nonlinear,time-variant or time-invariant.We focus on LTI system,that is linear time-invariant.系统可分为线性或非线性，时变或时不变。
15544+自动化专业英语(习题参考解答)
自动化专业英语姜书艳主编张昌华徐心皓何芳编著习题参考解答Unit 1A. Basic laws of Electrical Networks[EX.1] Comprehension1. KCL:The algebraic sum of the currents entering any node is zero.KVL:The algebraic sum of the voltage around any closed path is zero.2. Node: A point at which two or more elements have a common connection is calleda node.Branches: a single path in a network composed of one simple element and the node at each end of that element.Path: If no node was encountered more than once, then the set of nodes and elements that we have passed through is defined as a path.Loop: If the node at which we started is the same as the node on which we ended, then the path is, by definition, a closed path or a loop. a path is a particular collection of branches.3. 4, 5, We can form a path but not a loop.4. v R2=32V, V x=6V[EX.2] Translation from English to Chinese1. 如果定义具有最大连接支路数的节点为参考节点，那么得到的方程相对来说比较简单。
建设方案缩写英文
建设方案缩写英文引言在项目的开发过程中，往往会涉及到各种各样的方案和流程。
为了方便交流和沟通，我们通常会用缩写的方式来代替长串的英文单词。
本文将介绍一些常用的建设方案的缩写和英文翻译。
建设方案缩写下面是一些常用的建设方案缩写及其相应的英文翻译：1.PM - Project Management （项目管理）2.BA - Business Analysis （业务分析）3.RD - Research and Development （研发）4.DBA - Database Administrator （数据库管理员）5.UI - User Interface （用户界面）6.UX - User Experience （用户体验）7.QA - Quality Assurance （质量保证）8.CI/CD - Continuous Integration/Continuous Deployment （持续集成/持续部署）9.DevOps - Development Operations （开发运维）10.API - Application Programming Interface （应用程序编程接口）11.SDK - Software Development Kit （软件开发工具包）12.DNS - Domain Name System （域名系统）13.HTML - Hypertext Markup Language （超文本标记语言）14.CSS - Cascading Style Sheets （层叠样式表）15.HTTP - Hypertext Transfer Protocol （超文本传输协议）使用建设方案缩写的好处使用建设方案缩写有许多好处，特别是在项目团队中进行沟通和交流时：1.减少沟通成本：使用缩写可以简化长串的英文单词，减少交流中的不必要的冗长描述，节省时间和精力。
2.提高沟通效率：缩写可以快速传递信息，减少理解的障碍，提高团队成员之间的沟通效率。
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x1(t)*x2(t)=x2(t)*x1(t), the associative property [x1(t)*x2(t)]*x3(t)=x1(t)*[x2(t)*x3(t)], and the distributive property x1(t)*[x2(t)+x3(t)]=x1(t)*x2(t)+ x1(t)*x3(t). (1) Reflect x2(τ) about the origin to obtain x2(−τ). (2) Shift x2(−τ) by t to obtain x2(t−τ). (3) Calculate the convolution integral at t.
δ(t) has an important sampling property, i.e., x(t)δ(t−t0)=x(t0)δ(t−t0), where t0 is an arbitrary real number. 2.1.2. Continuous-Time Step Function The continuous-time step function is defined as (2.4)
2. Time-Domain Analysis of ContinuousTime Signals and Systems
2.1. Continuous-Time Impulse Function (1.4.2) 2.2. Convolution Integral (2.2) 2.3. Continuous-Time Impulse Response (2.2) 2.4. Classification of a Linear Time-Invariant ContinuousTime System by its Impulse Response (2.3) 2.5. Linear Constant-Coefficient Differential Equations (2.4.1)
(1) x1(t)=eatu(t), a<0 and x2(t)=u(t).
1, 0 < t < T t, 0 < t < 2T (2) x1 ( t ) = and x 2 ( t ) = . 0, otherwise 0, otherwise
(3) x1(t)=e2tu(−t) and x2(t)=u(t−3). 2.3. Continuous-Time Impulse Response 2.3.1. Definition of Continuous-Time Impulse Response A linear time-invariant continuous-time system can be completely characterized by the continuous-time impulse response, which is defined as the response of the system to the continuous-time impulse function. In addition, a linear time-invariant continuous-time system can be completely characterized by the continuous-time step response, which is defined as the response of the system to the continuous-time
h * (−t ) / | h (−t ) |, h( − t) ≠ 0 x(t) = , h( − t) = 0 0,
the output of the system at t=0 is
y(0) = ∫ x(τ)h(−τ)dτ = ∫
−∞ ∞ h ( − τ) ≠ 0 ∞
(2.22)
x(τ)h(−τ)dτ
2.1. Continuous-Time Impulse Function 2.1.1. Continuous-Time Impulse Function The continuous-time impulse function, δ(t), is defined by
∞ ∫−∞ δ( t )dt = 1 . δ( t ) = 0, t ≠ 0
δ(t) can be considered as
δ( t ) = lim δ ∆ ( t ),
∆ →0
(2.2)
where (figure 2.2)
∆ 1 , | t |≤ ∆ 2 . δ∆ (t ) = 0, | t |> ∆ 2
1/∆ δ∆(t)
(2.3)
t −∆/2 ∆/2 Figure 2.2. δ∆(t).
∞ −∞
(2.15)
By definition, h(t)=T[δ(t)]. Since the system is time-invariant, then h(t−τ)=T[δ(t−τ)]. Substituting (2.16) into (2.15), one obtains (2.12). 2.4. Classification of a Linear Time-Invariant Continuous-Time System by its Impulse Response 2.4.1. Memoryless Systems versus Systems with Memory Assume that h(t) is the impulse response of a linear time-invariant continuous-time system. The system is memoryless if and only if h(t)=0, t≠0. 2.4.2. Causal Systems versus Noncausal Systems Assume that h(t) is the impulse response of a linear time-invariant (2.17) (2.16)
∫
∞
−∞
h ( t ) dt ≤ B h .
(2.19)
Proof. Consider the sufficiency first. Let x(t) be bounded, i.e., |x(t)|≤Bx, where Bx is a finite constant. Then,
| y( t ) |=
(2.20)
∫
∞
−∞
h (τ)x (t − τ)dτ ≤ ∫ | h(τ) || x (t − τ) | dτ
−∞
∞
≤ Bx ∫ | h (τ) | dτ ≤ Bx Bh .
−∞
∞
(2.21)
That is, y(t) is also bounded. Thus, the system is stable. Consider the necessity next. For the input
(2.1)
The illustration of the continuous-time impulse function is given in figure 2.1. δ(t) 1 t t0 Figure 2.1. Illustration of Continuous-Time Impulse Function. Aδ(t−t0) A t
step function. 2.3.2. I/O Relation by Continuous-Time Impulse Response The I/O relation of a linear time-invariant continuous-time system can be expressed by its impulse response. Let x(t) and h(t) be the input and the impulse response of a linear time-invariant continuoustime system, respectively. Then, the output of the system will be y(t)=x(t)*h(t). Proof. Since
0, t < 0 u(t) = 1, t > 0
(figure 2.3). Note that u(t) is undefined at t=0. u(t) 1 t Figure 2.3. Continuous-Time Step Function.
(2.5)
u(t) can be expressed as the running integral of δ(t), i.e.,
(2.9)
(2.10)
(2.11)
The convolution integral can be calculated in the following steps.
Steps (2) and (3) often need to be carried out in different ways for different intervals of t. Example. Find x1(t)*x2(t), where
continuous-time system. The system is causal if and only if h(t)=0, t<0. 2.4.3. Stable Systems versus Unstable Systems Assume that h(t) is the impulse response of a linear time-invariant continuous-time system. The system is stable if and only if h(t) is absolutely integrable. That is to say, there is a finite constant Bh such that (2.18)