Design of fractional delay filter using discrete Fourier transform interpolation method
Accelerated plane-wave destruction
Accelerated plane-wave destructionZhonghuan Chen 1,Sergey Fomel 2,and Wenkai Lu 1INTRODUCTIONLocal slope fields have been widely used in geophysical applications,such as wave-field separation and denoising (Harlan et al.,1984;Fomel et al.,2007),antialiased seismic interpolation (Bardan,1987),seislet transform (Fomel and Liu,2010),velocity-independent NMO correction and imaging (Fomel,2007b ;Cooke et al.,2009),predictive painting (Fomel,2010),seismic attribute analysis (Marfurt et al.,1999),etc.Several tools exist for local slope estimation:local slant stack (Ottolini,1983;Harlan et al.,1984),complex trace analysis (Barnes,1996),multiwindow dip search (Marfurt,2006),local structure tensor (Fehmers and Höcker,2003;Hale,2007),and plane-wave destruction (Claerbout,1992;Fomel,2002).Plane-wave destruction (PWD)approximates the local wavefield by a local plane wave,and models it using a linear differential equation (Claerbout,1992).When plane-wave destruction is applied on discrete sampled seis-mic signals,the corresponding differential equation needs to be dis-cretized by finite differences.Claerbout (1992)used explicit finite differences.In this method,plane-wave approximation of the wave-field can be seen as applying a linear finite impulse response (FIR)filter to the wavefield.Slope estimation is equivalent to estimating a parameter of the FIR filter.A least-squares estimator of the local slope can be obtained by minimizing the prediction error of the fil-ter.To improve estimation performance of the explicit finite differ-ence scheme,Schleicher et al.(2009)proposed total least-squares estimation.The implicit finite difference scheme was applied to the differ-ential equation by Fomel (2002).Using an infinite impulse response (IIR)filter,known as the “Thiran allpass filter ”(Thiran,1971),to approximate the phase-shift operator,the plane-wave destruction equation becomes a nonlinear equation of the slope.An iterative algorithm was designed to estimate the slope.To improve stability in the iterative algorithm,a smoothing regularization (Fomel,2007a )of the increment can be applied at each iteration.Iterations of regular-ization can be time-consuming,however,particularly in the 3D case.In this paper,we prove that the plane-wave destruction equation is a polynomial equation of an unknown slope.In the case of a three-point approximation of Thiran ’s filter,the convergence results of the iterative algorithm can be analytically analyzed.In this case,we obtain an analytical estimator of the local slope and show that the smoothing regularization can be applied on the final estimator only once.This approach reduces the computational time signifi-cantly.We present 2D and 3D examples,which demonstrate that the proposed algorithm can obtain a slope-estimation result faster than the iterative algorithm,with a similar or even better accuracy.THEORYReview of PWDThe local plane wave can be represented by the following differ-ential equation (Claerbout,1992)Manuscript received by the Editor 23April 2012;revised manuscript received 7August 2012;published online 25January 2013.1Tsinghua University,Department of Automation,State Key Laboratory of Intelligent Technology and Systems,Tsinghua National Laboratory for Informa-tion Science and Technology,Beijing,China.E-mail:zhonghuanchen@;lwkmf@.2The University of Texas at Austin,Bureau of Economic Geology,Jackson School of Geosciences,Austin,Texas,USA.E-mail:sergey.fomel@beg.utexas .edu.©2013Society of Exploration Geophysicists.All rights reserved.V1GEOPHYSICS,VOL.78,NO.1(JANUARY-FEBRUARY 2013);P.V1–V9,9FIGS.,1TABLE.10.1190/GEO2012-0142.1D o w n l o a d e d 09/22/13 t o 221.226.175.186. R e d i s t r i b u t i o n s u b j e c t t o SE G l i c e n s e o r c o p y r i g h t ; s e e T e r m s o f U s e a t h t t p ://l i b r a r y .s e g .o r g /∂u ∂x þσ∂u ∂t¼0;(1)where σis the local slope in continuous space,with dimension of time/length.The wavefields observed at the two positions x 1,x 2have a time delay which is proportional to their distance,σj x 1−x 2j .In the sampled system with space and time intervals Δx and Δt ,we define the discrete space slope in the unit of Δt ∕Δx as p ¼σΔx ∕Δt .Because p is independent of the sampling interval,it can be directly used in irregular data set (in this case,the unit of the slopes becomes space-variant).The time delay between two adjacent positions is then the slope p Δtu ðx;t Þ¼u ðx þΔx;t þp Δt Þ:(2)With the Z transform applied along time and space directions,the above equation becomesð1−Z x Z p t ÞU ðZ x ;Z t Þ¼0;(3)where Z t is the unit time-shift operator,Z x denotes the unit space-shift operator,and U ðZ x ;Z t Þis the Z transform of u ðx;t Þ.Theoperator 1−Z x Z p t is the plane-wave ing Thiran ’sfractional delay filter H ðZ t Þ¼B ð1∕Z t ÞB ðZ t Þ(Thiran,1971)to approximate the time-shift operator Z p t ¼e j ωp ,where ωis the circular frequency,the plane-wave destructor can be expressed as (Fomel,2002),C ðp Þ¼B ðZ t Þ−Z x B 1Z t;(4)whereB ðZ t Þ¼X N k ¼−Nb k ðp ÞZ −k t ;(5)N is the order of the noncausal temporal filter,and b k ðp Þare func-tions of the local slope p .Equation 4is a 2D filter.Applying the filter at an arbitrary point in the wavefield,the plane-wave destruction equation 3becomes a nonlinear equation for the local slope pC ðp;Z x ;Z t ÞU ðZ x ;Z t Þ≈0:(6)An iterative method,such as Newton ’s method,can be applied to find the slope.In practice,wavefields are polluted by noise and the plane wave assumption may not hold true where faults and conflict-ing boundaries exist.To obtain a stable slope estimation,an addi-tional smoothing regularization process (Fomel,2007a )is needed at each step.The total computational cost of slope estimation by plane-wave destruction becomes O ðN d N f N l N n Þ,where N d is the size of the data,N f ¼2N þ1is the size of the filter,N l is the num-ber of linear iterations for regularization,and N n is the number of nonlinear iterations for solving equation 6.Typical values are N f ¼3,5,N l ¼10–50,and N n ¼5–10.Accelerated PWDGauss-Newton ’s iteration searches the solutions for nonlinearequation 6as follows:Let p k be the estimated slope at step k ,with estimating error (or destructive error)e k ¼C ðp k ÞU ðZ x ;Z t Þ.To findthe correct solution p k þ1that minimizes e k þ1,we need to find theincrement Δp k from the local linearizatione k þ1¼C ðp k ÞU ðZ x ;Z t ÞþC 0ðp k ÞU ðZ x ;Z t ÞΔp k ≈0;(7)where C 0ðp k Þis the derivative of C ðp Þat p k with respect to p .The iterative algorithm stops when a stationary point or a root of C ðp ÞU is reached.They are:•Points where C 0ðp k ÞU ¼0:When p k satisfies C 0ðp ÞU ¼0,then e k þ1¼e k ,and the Δp k dependency in equation 7is removed,stopping further iterations on p k .•Points where C ðp k ÞU ¼0and C 0ðp ÞU ≠0:In this case,Δp k ¼0,thus p k þ1¼p k ,eliminating the need for further improvements on p k .The iterative algorithm for equation 6may converge at different points,depending on the initial point that we chose;p 0¼0is a common practical choice for the initial solution.In this case,the iterative algorithm may converge to the least absolute root,which denotes the event with smallest dip angle.To analyze the convergence results,the maximally flat fractional delay filter (Thiran,1971;Zhang,2009)is designed with polyno-mial coefficientsb k ðp Þ¼ð2N Þ!ð2N Þ!ð4N Þ!ðN þk Þ!ðN −k Þ!Y N −1−km ¼0ðm −2N þp Þ×Y N −1þk m ¼0ðm −2N −p Þ:(8)Details on how to design the filter can be found in Appendix A .Because b k ðp Þis a polynomial of p ,expanding it,we get b k ðp Þ¼P 2N i ¼0c ki p iandB ðZ t ;p Þ¼X N k ¼−N X 2N i ¼0c ki Z −k t p i:(9)From equation 8,it is obvious that b k ðp Þ¼b −k ð−p Þ,thereforec ki ¼ð−1Þi c −k;i andB ðZ t ;p Þ¼B1Z t;−p :(10)Substituting the above two equations,the nonlinear equation 6becomes a 2N th°polynomial equation for pX 2N i ¼0a i p i ¼0;(11)and the coefficients of the polynomial plane-wave destruction canbe expressed asa i ¼½1−ð−1ÞiZ xX N k ¼−Nc ki Z −kt U;(12)which says that the coefficients of the polynomial PWD can be ob-tained by applying a 2D filter on the wavefield u .Moreover,the 2D filter can be decoupled into the cascade of two 1D directional filters;the temporal filter P N k ¼−N c ki Z −k t and the spatial filter 1−ð−1Þi Z x .V2Chen et al.D o w n l o a d e d 09/22/13 t o 221.226.175.186. R e d i s t r i b u t i o n s u b j e c t t o SE G l i c e n s e o r c o p y r i g h t ; s e e T e r m s o f U s e a t h t t p ://l i b r a r y .s e g .o r g /In the special case of N ¼1,we get a three-point approximation of B ðZ t Þ.It takes the following form (Fomel,2002)B ðZ t Þ¼ð1þp Þð2þp Þ12Z −1t þð2þp Þð2−p Þ6þð1−p Þð2−p Þ12Z t :(13)The plane-wave destruction equation 11is a quadratic equation.The coefficients a i ði ¼0;1;2Þcan be solved for and expressed asa i ¼112½1−ð−1Þi Z x v i ;(14)where v i are outputs of the following three-point temporal filtersv 0¼2ðZ −1t þ4þZ t ÞU;(15)v 1¼3ðZ t −Z −1t ÞU;(16)andv 2¼ðZ −1t −2þZ t ÞU:(17)In this case,the quadratic plane-wave destruction equation 11has one stationary point and two roots,which can be analytically ex-pressed as:f −a 12a 2;−a 1ÆffiffiffiDp 2a 2g ,where D ¼a 21−4a 0a 2.The plots in Figure 1show the convergence process of the itera-tive algorithm when we choose p 0¼0as the starting value.Geo-metrically when D ≤0,the iteration converges to the stationarypoint −a 12,as shown in Figure 1a .When D >0,it converges to the least absolute solution of equation 11.Figure 1b and 1c shows the convergence process to the least absolute solution in different cases.We can summarize the convergence result of the iterative algorithm as followsp ¼8>><>>:−a12a 2D ≤0−2a0a 1−ffiffiffiD p D >0;a 1<0−2a 0a 1þffiffiffiDpD >0;a 1>0:(18)As −2a 0a 1ffiffiffiD p ¼−a 1ÆffiffiffiDp 2a 2inthe above equation,we use−2a 0a 1ffiffiffiDp instead of −a 1ÆffiffiffiDp 2a 2to obtainbetter numerical stability.When the data is polluted by noise,to obtain a robust slope es-timation,we can combine the equations in a local window into the following equation setFp ≈g ;(19)where F is a normalized diagonal matrix and g is a vector.Their elements are denominators and numerators of equation 18,respec-tively.When we are solving the above equation set by least squares,we can use Tikhonov ’s regularization (Fomel,2002)or the shaping regularization (Fomel,2007a ,equation 13)to obtain a smooth solu-tion as followsp ¼H ½I þH T ðF T F −I ÞH −1H T F T g ;(20)where H is an appropriate smoothing operator.In this case,the reg-ularization runs only once;therefore,the computational cost isreduced to O ðN d N f N l Þ.In 3D applications,there are two polynomial PWD equations for inline and crossline slopes separately.Note that,using the decou-pling,inline,and crossline slope estimations can share the temporal filtering results in equations 15–17.We can obtain the coefficients of the crossline plane-wave destruction equation asa i ¼112½1−ð−1Þi Z y v i .(21)The five-point or longer approximations of B ðZ t Þcan achieve higher accuracy.Equation 6in this case becomes a higher-order polynomial equation (see details in Appendix A ),which can be solved numerically.However,there are multiple stationary points,and it is difficult to determine the right one analytically.For appli-cations that need five-point or higher accuracy,we suggest obtain-ing an initial slope estimation by the proposed three-point method and using it to make the iterative algorithm converge faster (to de-crease N n ).EXAMPLESSynthetic examplesTo test the performance of the proposed slope-estimation method,we generated a harmonic wave field with constant slope p 0¼0.3,shown in Figure 2.We added different scales of additive white Gaussian noise (AWGN)to the wave field,and estimated the slope by the proposed method.To compare with the iterative algorithm by Fomel (2002),the mean square error (MSE)is used as the criterionMSE ðp Þ¼E fðp −p 0Þ2g :(22)We use five iterations in the iterative method,N n ¼5.For the constant slope model,using a large smoothing window,theFigure 1.The iterative results of Newton ’s algorithm.The initial point is p 0¼0(solid circle),and the convergence result is marked by an empty circle:(a)when D ≤0,(b)when D >0and a 1a 2>0,(c)when D >0,and a 1a 2<0.Accelerated plane-wave destructionV3D o w n l o a d e d 09/22/13 t o 221.226.175.186. R e d i s t r i b u t i o n s u b j e c t t o SE G l i c e n s e o r c o p y r i g h t ; s e e T e r m s o f U s e a t h t t p ://l i b r a r y .s e g .o r g /smoothing regularization can converge faster (with less N l )and we can obtain a better estimation accuracy.For each method,we try the smoothing windows from 2to 200and show the mean square errors in Figure pared with the iterative method,the proposed method has better accuracy at the left upper (low SNR and small smoothing window)and worse accuracy at right bottom corner (high SNR and large smoothing window).We show the total runtime of all the noise scale data in Figure 4.For all smoothing windows in the regularization,the proposed method (solid line)only uses about one-fifth of the run time of the three-point (N ¼1)iterative method (dash line).A more complicated model from Claerbout (1999)and Fomel (2002)is shown in Figure 5a .It has variable slopes in synclines,anticlines,and faults.The slope estimated by the proposed method is shown in Figure 5b .The estimation takes about 20ms.The three-point (N ¼1)iterative method can obtain a similar estimation (shown in Figure 5c )by five iterations,which takes about 130ms.Bothmethods use a four-point smoothing window in the regularization,but the proposed method obtains a slightly smoother estimation.In Figure 5d ,we show the faults detected by the residuals of the pro-posed plane-wave destruction.ApplicationThe 2D seislet transform (Fomel and Liu,2010)uses local slopes to predict and update even and odd traces in the wavelet lifting scheme.The seislet transform itself is fast,but the slope estimation step is comparatively slow.The 3D seislet transform can be con-structed in the same way by using 3D slopes and cascading 2D transforms in inline and crossline directions.So that an efficient transform can be built,the proposed accelerated plane-wave de-struction is applied to slope estimation.Figure 6shows a part of the Teapot Dome image from Wyoming.The 3D slope estimation yields two slope fields along twospaceFigure 2.Harmonic waves with constant slope p 0¼0.3.a)b)Figure 3.Mean square errors of the slope estimations by the proposed method (a)and the three-point (N ¼1)iterative method(b).Figure 4.Run time of the proposed method (solid line)and the three-point (N ¼1)iterative method (dashed line).V4Chen et al.D o w n l o a d e d 09/22/13 t o 221.226.175.186. R e d i s t r i b u t i o n s u b j e c t t o SE G l i c e n s e o r c o p y r i g h t ; s e e T e r m s o f U s e a t h t t p ://l i b r a r y .s e g .o r g /directions.Figure7shows the local inline and crossline slope fields estimated by the proposed algorithm.The two slopes are used by the lifting scheme in the seislet trans-form to obtain the seislet transform coefficients.The coefficients of the2D seislet transform are concentrated at the planes near the zero inline plane,as shown in Figure8a,whereas in Figure8b,the3D transform coefficients are concentrated in the corner region near the origin.To illustrate the compressive performance of the3D seislet trans-form,Figure9shows the reconstruction results at different percen-tages of the compression.Most of the data can be reconstructed using only1%of the seislet coefficients(1∶100compression ratio). To compare with the iterative methods quantitatively,we define the following normalized crosscorrelation(NCC)NCCðx;yÞ¼x T yk x k2k y k2:(23)a)c)b)d)Figure5.2D slope estimation example:(a)synthetic data,(b)slope field estimated by the proposed algorithm,(c)slope field estimated by the iterative algorithmafter five iterations,(d)faults detection by plane-wave destruction with the estimated slope.Figure6.A portion of the3D data from the Teapot data set.Accelerated plane-wave destruction V5 Downloaded9/22/13to221.226.175.186.RedistributionsubjecttoSEGlicenseorcopyright;seeTermsofUseathttp://library.seg.org/Figure7.3D slopes estimated by the proposed algorithm:(a)inline slope(b)crossline slope.Figure8.Coefficients of:(a)the2D seislet transform along inline direction only,(b)the3D seislettransform.Figure9.Reconstruction of3D-seislet-compressed data using:(a)5%of the seislet coefficients,(b)1%of the seislet coefficients.V6Chen et al.Downloaded9/22/13to221.226.175.186.RedistributionsubjecttoSEGlicenseorcopyright;seeTermsofUseathttp://library.seg.org/In the seislet transform,the more accurate dip we use,the better compression we can obtain.The NCC between the reconstructed data and the original data can be used to quantify the compressive performance.In Table 1,the proposed method is compared with three-point (N ¼1)and five-point (N ¼2)iterative methods.In all three methods,we use 10-point smoothing windows in in-line and crossline dimensions,and use five-point smoothing win-dow in time direction.To obtain a similar slope estimation as the proposed method,the three-point (N ¼1)and five-point (N ¼2)iterative methods need about six and five iterations,respectively.The five-point method can obtain a better compression ratio than the three-point method because of its better accuracy in slope es-timation.However,although the iterative methods have smaller PWD residuals,neither of them achieves a better NCC than the proposed method.In this case,using the noniterative estimation as the initial in five-point estimation can save at least 250s.That is to say,the computational time cost is reduced by a factor of about six.CONCLUSIONSIn this paper,we derived an analytical estimator of the local slope in three-point implicit plane-wave destruction.On the basis of this result,we built an accelerated slope-estimation algorithm.Exam-ples show that the proposed method can produce a result that is similar to that of the iterative algorithm,at a reduced computation time.Two or more conflicting slopes can be estimated simultaneously by the iterative algorithm.In this case,the PWD equation is a multi-variable polynomial,and the convergence analysis becomes com-plicated.The proposed noniterative method is not yet suitable for multislope estimation.However,we believe that it can find many applications in situations where one dominant slope is suf-ficient.ACKNOWLEDGMENTSWe thank Alexander Klokov for his helpful technical sugges-tions.We also thank the reviewers and the editors for their carefulreview of the paper.The Teapot Dome data is provided by the Rocky Mountain Oilfield Testing Center,sponsored by the U.S.Department of Energy.Zhonghuan Chen ’s joint research is sponsored by the China Scholarship Council and China State Key Science and Technology Projects (2011ZX05023-005-007).APPENDIX APOLYNOMIAL FORM OF PWDIf all the coefficients of B ðZ t Þare polynomials of p ,equation 4is also a polynomial of p ,and the plane-wave destruction equation becomes in turn a polynomial equation of p .The problem is to de-sign a 2N þ1-points filter B ðZ t Þwith polynomial coefficients suchthat the all pass system H ðZ t Þ¼B ð1∕Z t ÞB ðZ t Þcan approximate the phase-shift operator Z p t ¼e j ωp .Denoting the phase response of the system as θðωÞ,that is H ðe j ωÞ¼e j θðωÞ,the group delay of the system isτðωÞ¼∂θðωÞ∂ω:(A-1)The maximally flat criteria designs a filter with a smoothest phase response.There are 2N unknown coefficients in H ðZ t Þ,so we can add 2N flat constraints for the first 2N -th order deviratives of the phase response.It becomes (Zhang,2009,equation 7)τðωÞ¼p ∂n τðωÞ∂ωn ¼0n ¼1;2;:::;2N;(A-2)which is equivalent to the following linear maximally flat condi-tions (Thiran,1971)X N k ¼−Nðd −k Þ2n þ1b k ¼0;(A-3)where n ¼0;1;:::;2N −1and d ¼p ∕2is the fractional delay of B ð1∕Z t Þor 1∕B ðZ t Þ.To solve b k from the above equations,Thiran (1971)used an ad-ditional condition b 0¼1,which leads b k ðk ≠0Þto be a fractional function of p .Differently from that,we use the following condition,X N k ¼−Nb k ¼1;(A-4)where b k can be proved to be polynomials of p .Let vector b ¼½b 0;b N ;:::;b 1;b −1;:::;b −N T .Combining equations A-3and A-4,we rewrite them into the following matrix formTable 1.Performance of different dip estimation methods in 3D seislet transform:Runtime is the runtime of the slope estimation process;RES-inline is the inline residual;RES-xline is the crossline residual;NCC-1is the normalized crosscorrelation between the original data and the reconstruction using 1%of the seislet coefficients;NCC-5uses 5%of the coefficients.The run time for 2D and 3D seislet transform are about 22.45s and 45.0s,respectively.Method N IterationsRuntime (s)RES-inline RES-xline NCC-1NCC-5Noniterative 1054.630.23140.22420.88580.9618Iterative 16334.50.22670.21720.88140.961Iterative25301.60.21940.20750.88380.9615Accelerated plane-wave destruction V7D o w n l o a d e d 09/22/13 t o 221.226.175.186. R e d i s t r i b u t i o n s u b j e c t t o SE G l i c e n s e o r c o p y r i g h t ; s e e T e r m s o f U s e a t h t t p ://l i b r a r y .s e g .o r g /266666411:::11:::1d d −N :::d −1d þ1:::d þN d 3ðd −N Þ3:::ðd −1Þ3ðd þ1Þ3:::ðd þN Þ3......::::::::::::...d 2N −1ðd −N Þ4N −1:::ðd −1Þ4N −1ðd þ1Þ4N −1:::ðd þN Þ2N −13777775×b ¼2666664100 03777775:The matrix on the left side,denoted as V ,can be split into four blocksA B C Das shown above.Following the lemma of matrix inversion,V −1¼ðA −BD −1C Þ−1−ðA −BD −1C Þ−1D −1−D −1C ðA −BD −1C Þ−1D −1þD −1ðA −BD −1C Þ−1BD −1;(A-5)therefore,the coefficientsb ¼V −1½1;0;:::;0 T¼ ðA −BD −1C Þ−1−D −1C ðA −BD −1C Þ−1:(A-6)Let subindex i ¼−N;−N þ1;:::;−1;1;2;:::;N andx i ¼d þi .Submatrix D can be expressed asD ¼EX¼26666641:::11:::1ðd −N Þ2:::ðd −1Þ2ðd þ1Þ2:::ðd −N Þ2ðd −N Þ4:::ðd −1Þ4ðd þ1Þ4:::ðd þN Þ4...:::......:::...ðd −N Þ4N −2:::ðd −1Þ4N −2ðd þ1Þ4N −2:::ðd þN Þ4N −23777775×diag 2666666664x −N ...x −1x 1...x N3777777775;so D −1¼X −1E −1.Denoting U ¼E −1with elements u ij ,j ¼1;2;:::;2N ,as E is a Vandermonde matrix,u ij and Lagrange intepolating polynomials have the following relationshipX 2N j ¼1u ij x 2j −2¼l i ðx Þ;(A-7)where i ¼−N;:::;−1;1;:::;N ,and l i ðx Þis the Lagrange poly-nomial related to the basis d þi ,l i ðx Þ¼Ym ≠i;m ≠0−N ≤m ≤Nx 2−ðd þm Þ2ðd þi Þ2−ðd þm Þ2:(A-8)Substituting the above equation,u ij and x into equation A-7,we can prove equation A-7.It follows that½E −1C i ¼d l i ðd Þ;(A-9)½D −1C i ¼½X −1E −1C i ¼dd þi l iðd Þ;(A-10)withl i ðd Þ¼ð−1Þi þ1N !N !ðN þi Þ!ðN −i Þ!d þi d Y Nm ¼−N 2d þm2d þm þi:(A-11)Thus,A −BD −1C ¼XN i ¼−Nð−1ÞiN !N !ðN þi Þ!ðN −i Þ!Y N m ¼−N p þmp þm þi ¼ð4N Þ!N !N !1Q m ¼N þ1(A-12)and½A −BD −1C −1¼ð2N Þ!ð2N Þ!ð4N Þ!N !N !Y 2Nm ¼N þ1ðm 2−p 2Þ:(A-13)It is the coefficient b 0,a 2N th°polynomial of p .Substituting it into equation A-6,the coefficients at k ¼Æ1;Æ2;:::ÆN are expressed asb k ¼−½D −1C k ½A −BD −1C −1¼ð2N Þ!ð2N Þ!ð4N Þ!ðN þk Þ!ðN −k Þ!Y N −1−km ¼0ðm −2N þp Þ×Y N −1þk m ¼0ðm −2N −p Þ:(A-14)With the additional condition A-4in 2N þ1points approxima-tion,all the coefficients are polynomials of p of 2N th°.Thus,theplane-wave destruction equation 6is proved to be a polynomial equation of 2N th°.REFERENCESBardan,V .,1987,Trace interpolation in seismic data processing:Geo-physical Prospecting,35,343–358,doi:10.1111/j.1365-2478.1987.tb00822.x .Barnes,A.E.,1996,Theory of 2-D complex seismic trace analysis:Geo-physics,61,264–272,doi:10.1190/1.1443947.Claerbout,J.F.,1992,Earth soundings analysis:Processing versus inver-sion:Blackwell Scientific Publications,/sep/prof/index.html ,accessed 10October 2012.V8Chen et al.D o w n l o a d e d 09/22/13 t o 221.226.175.186. R e d i s t r i b u t i o n s u b j e c t t o SE G l i c e n s e o r c o p y r i g h t ; s e e T e r m s o f U s e a t h t t p ://l i b r a r y .s e g .o r g /。
farrow结构的分数延迟滤波器
farrow结构的分数延迟滤波器
"Farrows 结构" 是一种用于实现分数延迟滤波器（Fractional Delay Filter）的一种结构。
分数延迟滤波器是一类用于在信号处理中引入精确和可变延迟的滤波器。
Farrows 结构常常被用于实现这种类型的滤波器。
Farrows 结构的关键特点是能够以分数的精度提供延迟，这对于许多信号处理应用非常重要，例如音频处理、通信系统等。
这个结构通常使用插值技术，例如线性插值，以提供连续的、精确的延迟。
Farrows 结构的基本思想是使用一个滤波器来产生一个带有延迟效果的信号，并通过插值来获得所需的分数延迟。
这个结构一般包含了一组延迟单元和一个插值滤波器。
具体的Farrows 结构的实现可能会涉及到一些数学和信号处理的细节，因此具体的算法和代码可能会有所不同，具体取决于应用的需求和设计。
matlab工具箱安装教程
1.1 如果是Matlab安装光盘上的工具箱，重新执行安装程序，选中即可；1.2 如果是单独下载的工具箱，一般情况下仅需要把新的工具箱解压到某个目录。
2 在matlab的file下面的set path把它加上。
3 把路径加进去后在file→Preferences→General的Toolbox Path Caching里点击update Toolbox Path Cache更新一下。
4 用which newtoolbox_command.m来检验是否可以访问。
如果能够显示新设置的路径，则表明该工具箱可以使用了。
把你的工具箱文件夹放到安装目录中“toolbox”文件夹中，然后单击“file”菜单中的“setpath”命令，打开“setpath”对话框，单击左边的“ADDFolder”命令，然后选择你的那个文件夹，最后单击“SAVE”命令就OK了。
MATLAB Toolboxes＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝/zsmcode.htmlBinaural-modeling software for MATLAB/Windows/home/Michael_Akeroyd/download2.htmlStatistical Parametric Mapping (SPM)/spm/ext/BOOTSTRAP MATLAB TOOLBOX.au/downloads/bootstrap_toolbox.htmlThe DSS package for MATLABDSS Matlab package contains algorithms for performing linear, deflation and symmetric DSS. http://www.cis.hut.fi/projects/dss/package/Psychtoolbox/download.htmlMultisurface Method Tree with MATLAB/~olvi/uwmp/msmt.htmlA Matlab Toolbox for every single topic !/~baum/toolboxes.htmleg. BrainStorm - MEG and EEG data visualization and processingCLAWPACK is a software package designed to compute numerical solutions to hyperbolic partial differential equations using a wave propagation approach/~claw/DIPimage - Image Processing ToolboxPRTools - Pattern Recognition Toolbox (+ Neural Networks)NetLab - Neural Network ToolboxFSTB - Fuzzy Systems ToolboxFusetool - Image Fusion Toolboxhttp://www.metapix.de/toolbox.htmWAVEKIT - Wavelet ToolboxGat - Genetic Algorithm ToolboxTSTOOL is a MATLAB software package for nonlinear time series analysis.TSTOOL can be used for computing: Time-delay reconstruction, Lyapunov exponents, Fractal dimensions, Mutual information, Surrogate data tests, Nearest neighbor statistics, Return times, Poincare sections, Nonlinear predictionhttp://www.physik3.gwdg.de/tstool/MATLAB / Data description toolboxA Matlab toolbox for data description, outlier and novelty detectionMarch 26, 2004 - D.M.J. Taxhttp://www-ict.ewi.tudelft.nl/~davidt/dd_tools/dd_manual.htmlMBEhttp://www.pmarneffei.hku.hk/mbetoolbox/Betabolic network toolbox for Matlabhttp://www.molgen.mpg.de/~lieberme/pages/network_matlab.htmlPharmacokinetics toolbox for Matlabhttp://page.inf.fu-berlin.de/~lieber/seiten/pbpk_toolbox.htmlThe SpiderThe spider is intended to be a complete object orientated environment for machine learning in Matlab. Aside from easy use of base learning algorithms, algorithms can be plugged together and can be compared with, e.g model selection, statistical tests and visual plots. This gives all the power of objects (reusability, plug together, share code) but also all the power of Matlab for machine learning research.http://www.kyb.tuebingen.mpg.de/bs/people/spider/index.htmlSchwarz-Christoffel Toolbox/matlabcentral/fileexchange/loadFile.do?objectId=1316&objectT ype=file#XML Toolbox/matlabcentral/fileexchange/loadFile.do?objectId=4278&object Type=fileFIR/TDNN Toolbox for MATLABBeta version of a toolbox for FIR (Finite Impulse Response) and TD (Time Delay) NeuralNetworks./interval-comp/dagstuhl.03/oish.pdfMisc.http://www.dcsc.tudelft.nl/Research/Software/index.htmlAstronomySaturn and Titan trajectories ... MALTAB astronomy/~abrecht/Matlab-codes/AudioMA Toolbox for Matlab Implementing Similarity Measures for Audiohttp://www.oefai.at/~elias/ma/index.htmlMAD - Matlab Auditory Demonstrations/~martin/MAD/docs/mad.htmMusic Analysis - Toolbox for Matlab : Feature Extraction from Raw Audio Signals for Content-Based Music Retrihttp://www.ai.univie.ac.at/~elias/ma/WarpTB - Matlab Toolbox for Warped DSPBy Aki Härmä and Matti Karjalainenhttp://www.acoustics.hut.fi/software/warp/MATLAB-related Softwarehttp://www.dpmi.tu-graz.ac.at/~schloegl/matlab/Biomedical Signal data formats (EEG machine specific file formats with Matlab import routines)http://www.dpmi.tu-graz.ac.at/~schloegl/matlab/eeg/MPEG Encoding library for MATLAB Movies (Created by David Foti)It enables MATLAB users to read (MPGREAD) or write (MPGWRITE) MPEG movies. That should help Video Quality project.Filter Design packagehttp://www.ee.ryerson.ca:8080/~mzeytin/dfp/index.htmlOctave by Christophe COUVREUR (Generates normalized A-weigthing, C-weighting, octave and one-third-octave digital filters)/matlabcentral/fileexchange/loadFile.do?objectType=file&object Id=69Source Coding MATLAB Toolbox/users/kieffer/programs.htmlBio Medical Informatics (Top)CGH-Plotter: MATLAB Toolbox for CGH-data AnalysisCode: http://sigwww.cs.tut.fi/TICSP/CGH-Plotter/Poster: http://sigwww.cs.tut.fi/TICSP/CSB2003/Posteri_CGH_Plotter.pdfThe Brain Imaging Software Toolboxhttp://www.bic.mni.mcgill.ca/software/MRI Brain Segmentation/matlabcentral/fileexchange/loadFile.do?objectId=4879Chemometrics (providing PCA) (Top)Matlab Molecular Biology & Evolution Toolbox(Toolbox Enables Evolutionary Biologists to Analyze and View DNA and Protein Sequences) James J. 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Chen/support/books/book5295.jsp?category=new&language=-1MATLAB M-files and Simulink models/matlabcentral/fileexchange/loadFile.do?objectId=3834&object Type=file•OPNML/MATLAB Facilities/OPNML_Matlab/Mesh Generation/home/vavasis/qmg-home.htmlOpenFEM : An Open-Source Finite Element Toolbox/CALFEM is an interactive computer program for teaching the finite element method (FEM)http://www.byggmek.lth.se/Calfem/frinfo.htmThe Engineering Vibration Toolbox/people/faculty/jslater/vtoolbox/vtoolbox.htmlSaGA - Spatial and Geometric Analysis Toolboxby Kirill K. Pankratov/~glenn/kirill/saga.htmlMexCDF and NetCDF Toolbox For Matlab-5&6/staffpages/cdenham/public_html/MexCDF/nc4ml5.htmlCUEDSID: Cambridge University System Identification Toolbox/jmm/cuedsid/Kriging Toolbox/software/Geostats_software/MATLAB_KRIGING_TOOLBOX.htmMonte Carlo (Dr Nando)http://www.cs.ubc.ca/~nando/software.htmlRIOTS - The Most Powerful Optimal Control Problem Solver/~adam/RIOTS/ExcelMATLAB xlsheets/matlabcentral/fileexchange/loadFile.do?objectId=4474&objectTy pe=filewrite2excel/matlabcentral/fileexchange/loadFile.do?objectId=4414&objectTy pe=fileFinite Element Modeling (FEM) (Top)OpenFEM - An Open-Source Finite Element Toolbox/NLFET - nonlinear finite element toolbox for MATLAB ( framework for setting up, solving, and interpreting results for nonlinear static and dynamic finite element analysis.)/GetFEM - C++ library for finite element methods elementary computations with a Matlabinterfacehttp://www.gmm.insa-tlse.fr/getfem/FELIPE - FEA package to view results ( contains neat interface to MATLA/~blstmbr/felipe/Finance (Top)A NEW MATLAB-BASED TOOLBOX FOR COMPUTER AIDED DYNAMIC TECHNICAL TRADINGStephanos Papadamou and George StephanidesDepartment of Applied Informatics, University Of Macedonia Economic & Social Sciences, Thessaloniki, Greece/fen31/one_time_articles/dynamic_tech_trade_matlab6.htm Paper: :8089/eps/prog/papers/0201/0201001.pdfCompEcon Toolbox for Matlab/~pfackler/compecon/toolbox.htmlGenetic Algorithms (Top)The Genetic Algorithm Optimization Toolbox (GAOT) for Matlab 5/mirage/GAToolBox/gaot/Genetic Algorithm ToolboxWritten & distributed by Andy Chipperfield (Sheffield University, UK)/uni/projects/gaipp/gatbx.htmlManual: /~gaipp/ga-toolbox/manual.pdfGenetic and Evolutionary Algorithm Toolbox (GEATbx)/Evolutionary Algorithms for MATLAB/links/ea_matlab.htmlGenetic/Evolutionary Algorithms for MATLABhttp://www.systemtechnik.tu-ilmenau.de/~pohlheim/EA_Matlab/ea_matlab.html GraphicsVideoToolbox (C routines for visual psychophysics on Macs by Denis Pelli)/VideoToolbox/Paper: /pelli/pubs/pelli1997videotoolbox.pdf4D toolbox/~daniel/links/matlab/4DToolbox.htmlImages (Top)Eyelink Toolbox/eyelinktoolbox/Paper: /eyelinktoolbox/EyelinkToolbox.pdfCellStats: Automated statistical analysis of color-stained cell images in Matlabhttp://sigwww.cs.tut.fi/TICSP/CellStats/SDC Morphology Toolbox for MATLAB (powerful collection of latest state-of-the-art gray-scale morphological tools that can be applied to image segmentation, non-linear filtering, pattern recognition and image analysis)/Image Acquisition Toolbox/products/imaq/Halftoning Toolbox for MATLAB/~bevans/projects/halftoning/toolbox/index.htmlDIPimage - A Scientific Image Processing Toolbox for MATLABhttp://www.ph.tn.tudelft.nl/DIPlib/dipimage_1.htmlPNM Toolboxhttp://home.online.no/~pjacklam/matlab/software/pnm/index.htmlAnotherICA / KICA and KPCA (Top)ICA TU Toolboxhttp://mole.imm.dtu.dk/toolbox/menu.htmlMISEP Linear and Nonlinear ICA Toolboxhttp://neural.inesc-id.pt/~lba/ica/mitoolbox.htmlKernel Independant Component Analysis/~fbach/kernel-ica/index.htmMatlab: kernel-ica version 1.2KPCA- Please check the software section of kernel machines.KernelStatistical Pattern Recognition Toolboxhttp://cmp.felk.cvut.cz/~xfrancv/stprtool/MATLABArsenal A MATLAB Wrapper for Classification/tmp/MATLABArsenal.htmMarkov (Top)MapHMMBOX 1.1 - Matlab toolbox for Hidden Markov Modelling using Max. Aposteriori EM Prerequisites: Matlab 5.0, Netlab. Last Updated: 18 March 2002./~parg/software/maphmmbox_1_1.tarHMMBOX 4.1 - Matlab toolbox for Hidden Markov Modelling using Variational Bayes Prerequisites: Matlab 5.0,Netlab. Last Updated: 15 February 2002../~parg/software/hmmbox_3_2.tar/~parg/software/hmmbox_4_1.tarMarkov Decision Process (MDP) Toolbox for MatlabKevin Murphy, 1999/~murphyk/Software/MDP/MDP.zipMarkov Decision Process (MDP) Toolbox v1.0 for MATLABhttp://www.inra.fr/bia/T/MDPtoolbox/Hidden Markov Model (HMM) Toolbox for Matlab/~murphyk/Software/HMM/hmm.htmlBayes Net Toolbox for Matlab/~murphyk/Software/BNT/bnt.htmlMedical (Top)EEGLAB Open Source Matlab Toolbox for Physiological Research (formerly ICA/EEG Matlabtoolbox)/~scott/ica.htmlMATLAB Biomedical Signal Processing Toolbox/Toolbox/Powerful package for neurophysiological data analysis ( Igor Kagan webpage)/Matlab/Unitret.htmlEEG / MRI Matlab Toolbox/Microarray data analysis toolbox (MDAT): for normalization, adjustment and analysis of gene expression_r data.Knowlton N, Dozmorov IM, Centola M. Department of Arthritis and Immunology, Oklahoma Medical Research Foundation, Oklahoma City, OK, USA 73104. We introduce a novel Matlab toolbox for microarray data analysis. This toolbox uses normalization based upon a normally distributed background and differential gene expression_r based on 5 statistical measures. The objects in this toolbox are open source and can be implemented to suit your application. AVAILABILITY: MDAT v1.0 is a Matlab toolbox and requires Matlab to run. MDAT is freely available at:/publications/2004/knowlton/MDAT.zipMIDI (Top)MIDI Toolbox version 1.0 (GNU General Public License)http://www.jyu.fi/musica/miditoolbox/Misc. (Top)MATLAB-The Graphing Tool/~abrecht/matlab.html3-D Circuits The Circuit Animation Toolbox for MATLAB/other/3Dcircuits/SendMailhttp://carol.wins.uva.nl/~portegie/matlab/sendmail/Coolplothttp://www.reimeika.ca/marco/matlab/coolplots.htmlMPI (Matlab Parallel Interface)Cornell Multitask Toolbox for MATLAB/Services/Software/CMTM/Beolab Toolbox for v6.5Thomas Abrahamsson (Professor, Chalmers University of Technology, Applied Mechanics,Göteborg, Sweden)http://www.mathworks.nl/matlabcentral/fileexchange/loadFile.do?objectId=1216&objectType =filePARMATLABNeural Networks (Top)SOM Toolboxhttp://www.cis.hut.fi/projects/somtoolbox/Bayes Net Toolbox for Matlab/~murphyk/Software/BNT/bnt.htmlNetLab/netlab/Random Neural Networks/~ahossam/rnnsimv2/ftp: ftp:///pub/contrib/v5/nnet/rnnsimv2/NNSYSID Toolbox (tools for neural network based identification of nonlinear dynamic systems) http://www.iau.dtu.dk/research/control/nnsysid.htmlOceanography (Top)WAFO. Wave Analysis for Fatigue and Oceanographyhttp://www.maths.lth.se/matstat/wafo/ADCP toolbox for MATLAB (USGS, USA)Presented at the Hydroacoustics Workshop in Tampa and at ADCP's in Action in San Diego /operations/stg/pubs/ADCPtoolsSEA-MAT - Matlab Tools for Oceanographic AnalysisA collaborative effort to organize and distribute Matlab tools for the Oceanographic Community /Ocean Toolboxhttp://www.mar.dfo-mpo.gc.ca/science/ocean/epsonde/programming.htmlEUGENE D. GALLAGHER(Associate Professor, Environmental, Coastal & Ocean Sciences)/edgwebp.htmOptimization (Top)MODCONS - a MATLAB Toolbox for Multi-Objective Control System Design/mecheng/jfw/modcons.htmlLazy Learning Packagehttp://iridia.ulb.ac.be/~lazy/SDPT3 version 3.02 -- a MATLAB software for semidefinite-quadratic-linear programming .sg/~mattohkc/sdpt3.htmlMinimum Enclosing Balls: Matlab Code/meb/SOSTOOLS Sum of Squares Optimi zation Toolbox for MATLAB User’s guide/sostools/sostools.pdfPSOt - a Particle Swarm Optimization Toolbox for use with MatlabBy Brian Birge ... A Particle Swarm Optimization Toolbox (PSOt) for use with the Matlab scientific programming environment has been developed. PSO isintroduced briefly and then the use of the toolbox is explained with some examples. A link to downloadable code is provided.Plot/software/plotting/gbplot/Signal Processing (Top)Filter Design with Motorola DSP56Khttp://www.ee.ryerson.ca:8080/~mzeytin/dfp/index.htmlChange Detection and Adaptive Filtering Toolboxhttp://www.sigmoid.se/Signal Processing Toolbox/products/signal/ICA TU Toolboxhttp://mole.imm.dtu.dk/toolbox/menu.htmlTime-Frequency Toolbox for Matlabhttp://crttsn.univ-nantes.fr/~auger/tftb.htmlVoiceBox - Speech Processing Toolbox/hp/staff/dmb/voicebox/voicebox.htmlLeast Squared - Support Vector Machines (LS-SVM)http://www.esat.kuleuven.ac.be/sista/lssvmlab/WaveLab802 : the Wavelet ToolboxBy David Donoho, Mark Reynold Duncan, Xiaoming Huo, Ofer Levi /~wavelab/Time-series Matlab scriptshttp://wise-obs.tau.ac.il/~eran/MATLAB/TimeseriesCon.htmlUvi_Wave Wavelet Toolbox Home Pagehttp://www.gts.tsc.uvigo.es/~wavelets/index.htmlAnotherSupport Vector Machine (Top)MATLAB Support Vector Machine ToolboxDr Gavin CawleySchool of Information Systems, University of East Anglia/~gcc/svm/toolbox/LS-SVM - SISTASVM toolboxes/dmi/svm/LSVM Lagrangian Support Vector Machine/dmi/lsvm/Statistics (Top)Logistic regression/SAGA/software/saga/Multi-Parametric Toolbox (MPT) A tool (not only) for multi-parametric optimization. http://control.ee.ethz.ch/~mpt/ARfit: A Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive modelshttp://www.mat.univie.ac.at/~neum/software/arfit/The Dimensional Analysis Toolbox for MATLABHome: http://www.sbrs.de/Paper: http://www.isd.uni-stuttgart.de/~brueckner/Papers/similarity2002.pdfFATHOM for Matlab/personal/djones/PLS-toolbox/Multivariate analysis toolbox (N-way Toolbox - paper)http://www.models.kvl.dk/source/nwaytoolbox/index.aspClassification Toolbox for Matlabhttp://tiger.technion.ac.il/~eladyt/classification/index.htmMatlab toolbox for Robust Calibrationhttp://www.wis.kuleuven.ac.be/stat/robust/toolbox.htmlStatistical Parametric Mapping/spm/spm2.htmlEVIM: A Software Package for Extreme Value Analysis in Matlabby Ramazan Gençay, Faruk Selcuk and Abdurrahman Ulugulyagci, 2001.Manual (pdf file) evim.pdf - Software (zip file) evim.zipTime Series Analysishttp://www.dpmi.tu-graz.ac.at/~schloegl/matlab/tsa/Bayes Net Toolbox for MatlabWritten by Kevin Murphy/~murphyk/Software/BNT/bnt.htmlOther: /information/toolboxes.htmlARfit: A Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models/~tapio/arfit/M-Fithttp://www.ill.fr/tas/matlab/doc/mfit4/mfit.htmlDimensional Analysis Toolbox for Matlab/The NaN-toolbox: A statistic-toolbox for Octave and Matlab®... handles data with and without MISSING VALUES.http://www-dpmi.tu-graz.ac.at/~schloegl/matlab/NaN/Iterative Methods for Optimization: Matlab Codes/~ctk/matlab_darts.htmlMultiscale Shape Analysis (MSA) Matlab Toolbox 2000p.br/~cesar/projects/multiscale/Multivariate Ecological & Oceanographic Data Analysis (FATHOM)From David Jones/personal/djones/glmlab (Generalized Linear Models in 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分数时延滤波器设计
Abstract
Abstract
The fractional delay filter is a kind of digital filter whose sampling interval of delay is the fractional form. Generally, the way of design for the fractional delay filter is to approach the characteristics of the ideal fractional delay filter by scheme of designing suitable filter, and this filter is the expected fractional delay filter of the input signal. This paper will mainly introduce two kinds of design methods. The first kind is to design the fractional delay filter using the FIR digital filter, including that the methods of delay parameters is fixed, such as the least squared design method, Lagrange interpolation design method, equiripple design method and the methods of delay parameters is variable, such as Fourier Transform method and Farrow Structure method. Another kind is to design the fractional delay filter using the all-pass digital filter, including that the methods of delay parameters is fixed, such as the least squared design method, equiripple design method and the methods of delay parameters is variable, such as the Matrix Transform Method and Farrow Structure method. At the end of this paper, with the fractional delay filter for the wideband digital array beamforming of the wideband phased array radar for application cases. It will try to use two methods (multiphase structure method and FARROW structure method) to achieve the fractional delay filter, and these two kinds of methods also will be compared and summarized.
基于Farrow结构的宽带信号分数延时滤波器的FPGA设计与测试
火 控雷达技术
Ｆｉｒｅ Ｃｏｎｔｒｏｌ Ｒａｄａｒ Ｔｅｃｈｎｏｌｏｇｙ
Ｖｏ１．４５ Ｎｏ．２（Ｓｅｒｉｅｓ １７６）
Ｊｕｎ． ２０１６
z z z PsgiolePfrp
基 于 Ｆａｒｒｏｗ结 构 的宽 带 信 号 分 数 延 时 滤 波 器 的 ＦＰＧＡ设 计 与测 试
０ 引 言
宽带 相控 阵雷 达是 目前 雷达 技术 发展 的重 要方 向之一 。宽带信 号 可 以提 高 相控 阵雷 达 的抗 干 扰能 力 ，具 有更 高 的测 距 精度 及分 辨率 ，有 利于 目标 的成 像 、识别 与 分类 。但 传 统 的 相 位 控 制 方 法 由于 孑Ｌ径渡 越 问题会 导 致 波 束 的指 向偏 移 及 扫 描 不 准 ， 需要 采用 真 实 时 间延 时 线 （Ｔｒｕｅ Ｔｉｍｅ Ｄｅｌａｙ，ＴＴＤ） 来代 替移 相 器 。而 模 拟 延 迟 线 的成 本 高 、体 积 庞大 、功 耗 大 、稳 定 性 差 ，不 利 于 阵 列 雷 达 的应 用 。 数字 波 束 形 成 （Ｄｉｇｉｔａｌ Ｂｅａｍ Ｆｏｒｍｉｎｇ，ＤＢＦ）技 术 是
实现延 时补 偿具 有 成本低 、精 度 高、实现 简单 、稳 定性 好 等 众 多优 点 。 而基 于 Ｆａｒｒｏｗ结构 的 分数 延
时滤波 器 结构 简单 、延 时变化 灵活 快捷 ，且 易于构 建 宽带信 号 的分数 延 时滤 波 器。在 ＦＰＧＡ 系统 中
实现 宽带信 号 的分数 延 时 ，并 对其 延 时性 能 的 测 试 可 为将 来 宽 带信 号 的 ＤＢＦ工程 应 用 提 供技 术
基 础 。
关 键 词 ：数 字 波 束 形 成 ；Ｆａｒｒｏｗ结 构 ；分数 延 时
基于拉格朗日插值的分数延时滤波器研究
舰船电子对抗
SHIPBOARD ELECTRONIC COUNTERMEASURE
Oct.2018
Vol.41 No.5
基于拉格朗日插值的分数延时滤波器研究
黄 伟,周其超,陶存炳
(中国船舶重工集团公司第七二三研究所,江苏 扬州 225101)
摘要:分数延时滤波器可以在数字域实现对信号小数倍采样间隔时延,比传统模拟延迟线稳定、精度高,在数字 波 束
形成中应用广泛。基于拉格朗日插值的分 数 延 时 滤 波 器 实 现 简 单,低 频 具 有 很 好 的 幅 度 响 应 和 相 位 延 时 响 应。 介
绍了基于拉格朗日插值的分数延时滤波器的实现原理,仿真分析了 滤 波 器 的 幅 频 特 性 和 相 频 特 性,仿 真 结 果 表 明 拉
格朗日插值的分数延时滤波器用于信号的延时处理时具有良好的延时效果。
ResearchintoTheFractionalDelayFilterBasedonLagrangeInterpolation
HUANG Wei,ZHOU Qi-chao,TAO Cun-bing
(The723InstituteofCSIC,Yangzhou225101,China)
Abstract:Thefractionaldelayfiltercanrealizethefractionaltimessamplingintervaldelayofsignal indigitaldomain,whichismorestableandmoreaccuratethanthetraditionalanalogdelayline,and iswidelyusedindigitalbeamforming.ThefractionaldelayfilterbasedonLagrangeinterpolationis simpleandhasagoodamplituderesponseandphasedelayresponseinlowfrequency.ThispaperintroducestherealizationprincipleoffractionaldelayfilterbasedonLagrangeinterpolationmethod, simulatesandanalyzestheamplitude-frequencypropertyandthephase-frequencypropertyofthe filter.SimulationresultsshowthatthefractionaldelayfilterbasedonLagrangeinterpolationmethodhasagoodeffectintheapplicationofsignaldelayprocessing. Keywords:fractionaldelay;digitalbeamforming;digitalfilter;Lagrangeinterpolation method
DSP System Toolbox 80
Acoustic noise cancellation algorithm using System objects in MATLAB (above left). Filter coefficients can be plotted to display their values before adaptation (top right) and after adaptation (bottom right).DSP Algorithms for System Design and PrototypingDSP System Toolbox lets you mathematically model the behavior of your system and then simulate the model to accurately predict and optimize system performance. Using the system toolbox, you can simulate digital systems in MATLAB and Simulink. When you use the system toolbox in Simulink, you can also model advanced systems such as mixed-signal and multidomain systems.Algorithms in DSP System Toolbox serve as building blocks of signal processing systems in communications, audio, speech, RADAR, control systems, image and video processing, medical, and industrial applications. Algorithm Libraries for DSPAll algorithms in the system toolbox—whether implemented as MATLAB functions, MATLAB System objects or Simulink blocks—support double-precision and single-precision floating-point data types. Most also support integer and fixed-point data types (requires Fixed-Point Toolbox™or Simulink Fixed Point™).Algorithm categories in the system toolbox include:▪Signal operations such as convolution, windowing, padding, modeling delays, peak finding, and zero-crossing ▪Signal transforms such as fast Fourier transform (FFT), discrete cosine transform (DCT), short-time Fourier transform, and discrete wavelet transform (DWT)▪Filter design and implementation methods for digital FIR and IIR filters▪Statistical signal processing tools for signal analysis and spectral estimation▪Signal management methods such as buffering, indexing, switching, stacking, and queuing▪Linear algebra routines, including linear system solvers, matrix factorizations, and matrix inverses▪Scalar and vector quantizer encoding and decodingPartial list of System objects available in MATLAB (top) and category view of blocks available in Simulink (middle), with expanded views of the Signal Processing Sources and Transforms block libraries (bottom).Modeling Multirate SystemsDSP System Toolbox supports multirate processing for sample rate conversion and the modeling of systems in which different sample or clock rates need to be interfaced. Multirate functionality includes multirate filters and signal operations such as upsampling, downsampling, interpolation, decimation, and resampling.Sigma-delta A/D converter model in Simulink showing signals operating at multiple sample rates.Variable-Size SignalsDSP System Toolbox supports signal inputs that can change in size and value at run time. A subset of System objects and Simulink blocks provide support for variable-size signals that change size during the simulation or during distinct mode-switching events that occur in the initialization of conditionally executed subsystems. Support for variable-size signals enables you to model systems with varying resources, constraints, and environments.Adaptive, Multirate, and Specialized Filter Design MethodsDSP System Toolbox provides many methods for designing and implementing digital filters. You can design filters with lowpass, highpass, bandpass, bandstop, and other response types and realize them using filter structures such as direct-form FIR, overlap-add FIR, direct-form II with second-order sections, cascade allpass, and lattice structures.You can design filters in several ways:at the MATLAB command line, interactively using FDA Tool or Filterbuilder, or in Simulink using the filter design block library.The system toolbox supports a number of design methods, including:Advanced equiripple FIR filters,including minimum-order, constrained-ripple, minimum-phase designs Nyquist and halfband FIR and IIR filters,providing linear phase, minimum-phase, and quasi-linear phase (IIR) designs, as well as equiripple, sloped-stopband, and window methodsOptimized multistage designs,enabling you to optimize the number of cascaded stages to achieve the lowest computational complexityFractional-delay filters,including implementation using Farrow filter structures well-suited for tunable filteringapplicationsAllpass IIR filters with arbitrary group delay, enabling you to compensate for the group delays of other IIR filters to obtain an approximate linear phase passband responseLattice wave digital IIR filters,for robust fixed-point implementationArbitrary magnitude and phase FIR and IIR filters,enabling design of any filter specificationSpecialized filter designs in MATLAB showing LMS adaptive filter applied to a noisy music signal (top left), arbitrary magnitude filter design (top right), direct-form FIR filter responses for fixed-point data types (bottom left), and octave filter design (bottom right).Adaptive FiltersDSP System Toolbox provides several techniques for the design of adaptive filters: LMS-based, RLS-based, affine projection, fast transversal, frequency-domain, and lattice-based. The system toolbox also includes algorithms for the analysis of these filters, including tracking of coefficients, learning curves, and convergence.Multirate FiltersDSP System Toolbox provides functions for the design and implementation of multirate filters, including polyphase interpolators, decimators, sample-rate converters, and CIC filters and compensators, as well as support for multistage design methods. The system toolbox also provides specialized analysis functions to estimate the computational complexity of multirate filters.Interactive design of a lowpass filter in the Filterbuilder tool (left) and visualization of magnitude response (right).Specialized Filters for DSP ApplicationsDSP System Toolbox lets you design and implement specialized digital filters, including:▪Audio weighting filters, octave filters, and parametric equalizer filters for audio, speech, and acoustic applications▪Pulse shaping, peak or notch, and multirate filters for communications systems▪Kalman filters for aerospace and navigation systemsUsing Filters in Simulink System ModelsThe digital filters you design in DSP System Toolbox can also be used in system-level models in Simulink. MATLAB functions and System objects enable you to generate bit-true Simulink models from MATLAB filter designs. You can also use filter design block libraries in DSP System Toolbox to design, simulate, and implement filters directly in Simulink.Streaming and Frame-Based Signal ProcessingDSP System Toolbox enables the efficient simulation of real-time signal processing systems by supporting streaming signal processing and frame-based processing in MATLAB and Simulink.Streaming and frame-based processing techniques accelerate simulations by buffering input data into frames and processing multiple samples of data at a time. Faster simulations are achieved due to the distribution of the fixed process overhead across many samples. Although these techniques introduce a certain amount of latency in the system, in many instances you can select frame sizes that improve throughput without creating unacceptable latencies.In MATLAB, streaming signal processing is enabled by using System objects to represent data-driven algorithms, sources, and sinks. System objects implicitly manage many details of stream processing, such as data indexing,buffering, and algorithm state management. You can mix System objects with standard MATLAB functions andoperators. MATLAB programs that use System objects can be incorporated into Simulink models via the MATLAB Function block. Most System objects have corresponding Simulink blocks with the same capabilities.In Simulink, DSP System Toolbox blocks process input signals as frames when the specified input processing mode on the block dialog is set to frame-based processing. DSP System Toolbox supports sample-based processing for low latency processes and for applications that require scalar processing. Many blocks support both sample-based and frame-based processing modes.Envelope detection algorithm illustrating stream processing in MATLAB with System objects. Simulation results are shown for both the Hilbert transform and amplitude modulation methods of envelope detection.Signal Generation, I/O, and VisualizationGenerating and Importing SignalsThe signals that you work with can be acquired from a variety of sources. You can:▪Import audio signals from multimedia files▪Record audio data from soundcards▪Acquire multichannel audio data in real time▪Receive UDP packets from an IP network portSimulation results can be exported to audio files, audio devices, or transmitted as UDP packets over an IP network.You can also generate binary signals, random signals, and common waveforms such as sine waves and chirp signals using functions in DSP System Toolbox.Visualizing Signals in Time and Frequency DomainsDSP System Toolbox provides several tools for time-domain and frequency-domain visualization: Time Scope, Spectrum Scope, Vector Scope, and Waterfall Scope.Visualizing time-domain signals in the Time Scope tool. Simulation controls enable starting, pausing and stopping simulations from within the Time Scope.The Time Scope displays signals in the time-domain and supports a variety of signals—continuous and discrete, fixed-size and variable-size, floating and fixed-point data, and N-dimensional signals. You can also display multiple signals on the same axes, where each input signal has different dimensions, sample rates, and data types. Simulation controls on the Time Scope let you start, pause, continue, take a snapshot, or stop the simulation without having to switch windows.The Spectrum Scope estimates the spectrum of a time-domain input signal and displays its frequency spectrum on a linear or log scale. Scope parameters enable you to specify FFT length, buffer size and overlap, and spectrum units.The Vector Scope is a comprehensive display tool similar to a digital oscilloscope. You can use it to plot consecutive time samples from a vector or to plot vectors containing data such as filter coefficients or spectral magnitudes.The Waterfall Scope displays multiple vectors of data at one time, where each vector represents the input data at consecutive sample times. This tool only displays real-valued, double-precision data.Fixed-Point Implementation and Code Generation for DSP System ModelsYou can use DSP System Toolbox with Fixed-Point Toolbox or Simulink Fixed Point to model fixed-point signal processing algorithms and analyze the effects of quantization on system behavior and performance.Fixed-point support in the system toolbox includes:▪Word sizes from 1 to 128 bits▪Overflow handing and rounding methods▪Logging overflows, maxima, and minima of internal variables▪Manual or automatic scaling▪Data type override options to control system-level data type settingsFixed-Point Modeling and SimulationYou can configure System objects and blocks in the system toolbox for fixed-Point modes of operation, enabling you to perform design tradeoff analyses by running simulations with different word lengths, scaling, overflow handling, and rounding method choices before you commit to hardware.Fixed-point modes are supported for several DSP algorithms, including:▪FFT, DCT, IFFT, IDCT, and other signal transforms▪Digital Filter, Biquad Filter, LMS Filter, and other filter implementations▪Mean, Variance, Autocorrelation, Histogram, and other statistics▪Levinson-Durbin, Forward Substitution, Backward Substitution, and other linear system solvers▪Matrix Multiply, Matrix Product, Matrix Sum, Matrix 1-Norm, and other matrix operations▪Cumulative Product, Cumulative Sum, Difference, Normalization, and other math operationsIn Simulink, DSP System Toolbox automates the configuration of blocks for fixed-point operation. For example:▪Accumulator and multiplier sizes are specified to ensure compatibility for specific hardware targets.▪Binary point of a filter’s coefficient is automatically located based on user-defined word length, precision, and actual values.▪Product output retains all bits in the products between filter coefficients and input values.▪Accumulator is configured to avoid overflows.Block dialog for FFT block in DSP System Toolbox. The dialog provides options for fixed-point data type specification of accumulator, product, and output signals (requires Simulink Fixed-Point).Fixed-Point Filter DesignFilter design functions in DSP System Toolbox enable you to design floating-point filters that can be easily converted to fixed-point data types with Fixed-Point Toolbox. This design flow simplifies the design of fixed-point filters and lets you easily analyze quantization effects.Generating C and HDL CodeUsing DSP System Toolbox with MATLAB Coder and Simulink Coder, you can generate C code from your algorithms and system models. The generated code can be used for verification, rapid prototyping, and implementation of your system during the product development process.Using DSP System Toolbox with Filter Design HDL Coder™, you can generate HDL code from digital filter designs. In Simulink, DSP System Toolbox blocks provide support for HDL code generation when used withSimulink HDL Coder™.Product Details, Demos, and System Requirements/products/dsp-systemTrial Software/trialrequestSales/contactsalesTechnical Support/support ResourcesOnline User Community /matlabcentral Training Services /training Third-Party Products and Services /connections Worldwide Contacts /contact© 2011 The MathWorks, Inc. MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See /trademarksfor a list of additional trademarks. Other product or brand names may be trademarks or registered trademarks of their respective holders.11。
Matlab的第三方工具箱大全
Matlab的第三方工具箱大全(按住CTRL点击连接就可以到达每个工具箱的主页面来下载了)Matlab Toolboxes∙ADCPtools - acoustic doppler current profiler data processing∙AFDesign - designing analog and digital filters∙AIRES - automatic integration of reusable embedded software∙Air-Sea - air-sea flux estimates in oceanography∙Animation - developing scientific animations∙ARfit - estimation of parameters and eigenmodes of multivariate autoregressive methods∙ARMASA - power spectrum estimation∙AR-Toolkit - computer vision tracking∙Auditory - auditory models∙b4m - interval arithmetic∙Bayes Net - inference and learning for directed graphical models∙Binaural Modeling - calculating binaural cross-correlograms of sound∙Bode Step - design of control systems with maximized feedback∙Bootstrap - for resampling, hypothesis testing and confidence interval estimation ∙BrainStorm - MEG and EEG data visualization and processing∙BSTEX - equation viewer∙CALFEM - interactive program for teaching the finite element method∙Calibr - for calibrating CCD cameras∙Camera Calibration∙Captain - non-stationary time series analysis and forecasting∙CHMMBOX - for coupled hidden Markov modeling using max imum likelihood EM ∙Classification - supervised and unsupervised classification algorithms∙CLOSID∙Cluster - for analysis of Gaussian mixture models for data set clustering∙Clustering - cluster analysis∙ClusterPack - cluster analysis∙COLEA - speech analysis∙CompEcon - solving problems in economics and finance∙Complex - for estimating temporal and spatial signal complexities∙Computational Statistics∙Coral - seismic waveform analysis∙DACE - kriging approximations to computer models∙DAIHM - data assimilation in hydrological and hydrodynamic models∙Data Visualization∙DBT - radar array processing∙DDE-BIFTOOL - bifurcation analysis of delay differential equations∙Denoise - for removing noise from signals∙DiffMan - solv ing differential equations on manifolds∙Dimensional Analysis -∙DIPimage - scientific image processing∙Direct - Laplace transform inversion via the direct integration method∙DirectSD - analysis and design of computer controlled systems with process-oriented models∙DMsuite - differentiation matrix suite∙DMTTEQ - design and test time domain equalizer design methods∙DrawFilt - drawing digital and analog filters∙DSFWAV - spline interpolation with Dean wave solutions∙DWT - discrete wavelet transforms∙EasyKrig∙Econometrics∙EEGLAB∙EigTool - graphical tool for nonsymmetric eigenproblems∙EMSC - separating light scattering and absorbance by extended multiplicative signal correction∙Engineering Vibration∙FastICA - fixed-point algorithm for ICA and projection pursuit∙FDC - flight dynamics and control∙FDtools - fractional delay filter design∙FlexICA - for independent components analysis∙FMBPC - fuzzy model-based predictive control∙ForWaRD - Fourier-wavelet regularized deconvolution∙FracLab - fractal analysis for signal processing∙FSBOX - stepwise forward and backward selection of features using linear regression∙GABLE - geometric algebra tutorial∙GAOT - genetic algorithm optimization∙Garch - estimating and diagnosing heteroskedasticity in time series models∙GCE Data - managing, analyzing and displaying data and metadata stored using the GCE data structure specification∙GCSV - growing cell structure visualization∙GEMANOVA - fitting multilinear ANOVA models∙Genetic Algorithm∙Geodetic - geodetic calculations∙GHSOM - growing hierarchical self-organizing map∙glmlab - general linear models∙GPIB - wrapper for GPIB library from National Instrument∙GTM - generative topographic mapping, a model for density modeling and data visualization∙GVF - gradient vector flow for finding 3-D object boundaries∙HFRadarmap - converts HF radar data from radial current vectors to total vectors ∙HFRC - importing, processing and manipulating HF radar data∙Hilbert - Hilbert transform by the rational eigenfunction expansion method∙HMM - hidden Markov models∙HMMBOX - for hidden Markov modeling using maximum likelihood EM∙HUTear - auditory modeling∙ICALAB - signal and image processing using ICA and higher order statistics∙Imputation - analysis of incomplete datasets∙IPEM - perception based musical analysisJMatLink - Matlab Java classesKalman - Bayesian Kalman filterKalman Filter - filtering, smoothing and parameter estimation (using EM) for linear dynamical systemsKALMTOOL - state estimation of nonlinear systemsKautz - Kautz filter designKrigingLDestimate - estimation of scaling exponentsLDPC - low density parity check codesLISQ - wavelet lifting scheme on quincunx gridsLKER - Laguerre kernel estimation toolLMAM-OLMAM - Levenberg Marquardt with Adaptive Momentum algorithm for training feedforward neural networksLow-Field NMR - for exponential fitting, phase correction of quadrature data and slicing LPSVM - Newton method for LP support vector machine for machine learning problems LSDPTOOL - robust control system design using the loop shaping design procedure LS-SVMlabLSVM - Lagrangian support vector machine for machine learning problemsLyngby - functional neuroimagingMARBOX - for multivariate autogressive modeling and cross-spectral estimation MatArray - analysis of microarray dataMatrix Computation- constructing test matrices, computing matrix factorizations, visualizing matrices, and direct search optimizationMCAT - Monte Carlo analysisMDP - Markov decision processesMESHPART - graph and mesh partioning methodsMILES - maximum likelihood fitting using ordinary least squares algorithmsMIMO - multidimensional code synthesisMissing - functions for handling missing data valuesM_Map - geographic mapping toolsMODCONS - multi-objective control system designMOEA - multi-objective evolutionary algorithmsMS - estimation of multiscaling exponentsMultiblock - analysis and regression on several data blocks simultaneously Multiscale Shape AnalysisMusic Analysis - feature extraction from raw audio signals for content-based music retrievalMWM - multifractal wavelet modelNetCDFNetlab - neural network algorithmsNiDAQ - data acquisition using the NiDAQ libraryNEDM - nonlinear economic dynamic modelsNMM - numerical methods in Matlab textNNCTRL - design and simulation of control systems based on neural networks NNSYSID - neural net based identification of nonlinear dynamic systemsNSVM - newton support vector machine for solv ing machine learning problems NURBS - non-uniform rational B-splinesN-way - analysis of multiway data with multilinear modelsOpenFEM - finite element developmentPCNN - pulse coupled neural networksPeruna - signal processing and analysisPhiVis- probabilistic hierarchical interactive visualization, i.e. functions for visual analysis of multivariate continuous dataPlanar Manipulator - simulation of n-DOF planar manipulatorsPRT ools - pattern recognitionpsignifit - testing hyptheses about psychometric functionsPSVM - proximal support vector machine for solving machine learning problems Psychophysics - vision researchPyrTools - multi-scale image processingRBF - radial basis function neural networksRBN - simulation of synchronous and asynchronous random boolean networks ReBEL - sigma-point Kalman filtersRegression - basic multivariate data analysis and regressionRegularization ToolsRegularization Tools XPRestore ToolsRobot - robotics functions, e.g. kinematics, dynamics and trajectory generation Robust Calibration - robust calibration in statsRRMT - rainfall-runoff modellingSAM - structure and motionSchwarz-Christoffel - computation of conformal maps to polygonally bounded regions SDH - smoothed data histogramSeaGrid - orthogonal grid makerSEA-MAT - oceanographic analysisSLS - sparse least squaresSolvOpt - solver for local optimization problemsSOM - self-organizing mapSOSTOOLS - solving sums of squares (SOS) optimization problemsSpatial and Geometric AnalysisSpatial RegressionSpatial StatisticsSpectral MethodsSPM - statistical parametric mappingSSVM - smooth support vector machine for solving machine learning problems STATBAG - for linear regression, feature selection, generation of data, and significance testingStatBox - statistical routinesStatistical Pattern Recognition - pattern recognition methodsStixbox - statisticsSVM - implements support vector machinesSVM ClassifierSymbolic Robot DynamicsTEMPLAR - wavelet-based template learning and pattern classificationTextClust - model-based document clusteringTextureSynth - analyzing and synthesizing visual texturesTfMin - continous 3-D minimum time orbit transfer around EarthTime-Frequency - analyzing non-stationary signals using time-frequency distributions Tree-Ring - tasks in tree-ring analysisTSA - uni- and multivariate, stationary and non-stationary time series analysisTSTOOL - nonlinear time series analysisT_Tide - harmonic analysis of tidesUTVtools - computing and modifying rank-revealing URV and UTV decompositions Uvi_Wave - wavelet analysisvarimax - orthogonal rotation of EOFsVBHMM - variation Bayesian hidden Markov modelsVBMFA - variational Bayesian mixtures of factor analyzersVMT- VRML Molecule Toolbox, for animating results from molecular dynamics experimentsVOICEBOXVRMLplot - generates interactive VRML 2.0 graphs and animationsVSVtools - computing and modifying symmetric rank-revealing decompositions WAFO - wave analysis for fatique and oceanographyWarpTB - frequency-warped signal processingWAVEKIT - wavelet analysisWaveLab - wavelet analysisWeeks - Laplace transform inversion via the Weeks methodWetCDF - NetCDF interfaceWHMT - wavelet-domain hidden Markov tree modelsWInHD - Wavelet-based inverse halftoning via deconvolutionWSCT - weighted sequences clustering toolkitXMLTree - XML parserYAADA - analyze single particle mass spectrum dataZMAP - quantitative seismicity analysis。
用MATLAB的时重要MATLAB tools
用MATLAB的时重要MATLAB toolsADCPtools - acoustic doppler current profiler data processingAFDesign - designing analog and digital filtersAIRES - automatic integration of reusable embedded softwareAir-Sea - air-sea flux estimates in oceanographyAnimation - developing scientific animationsARfit - estimation of parameters and eigenmodes of multivariate autoregressive methodsARMASA - power spectrum estimationAR-Toolkit - computer vision trackingAuditory - auditory modelsb4m - interval arithmeticBayes Net - inference and learning for directed graphical modelsBinaural Modeling - calculating binaural cross-correlograms of soundBode Step - design of control systems with maximized feedbackBootstrap - for resampling, hypothesis testing and confidence interval estimationBrainStorm - MEG and EEG data visualization and processingBSTEX - equation viewerCALFEM - interactive program for teaching the finite element methodCalibr - for calibrating CCD camerasCamera CalibrationCaptain - non-stationary time series analysis and forecastingCHMMBOX - for coupled hidden Markov modeling using maximum likelihood EM Classification - supervised and unsupervised classification algorithmsCLOSIDCluster - for analysis of Gaussian mixture models for data set clusteringClustering - cluster analysisClusterPack - cluster analysisCOLEA - speech analysisCompEcon - solving problems in economics and financeComplex - for estimating temporal and spatial signal complexitiesComputational StatisticsCoral - seismic waveform analysisDACE - kriging approximations to computer modelsDAIHM - data assimilation in hydrological and hydrodynamic modelsData VisualizationDBT - radar array processingDDE-BIFTOOL - bifurcation analysis of delay differential equationsDenoise - for removing noise from signalsDiffMan - solving differential equations on manifoldsDimensional Analysis -DIPimage - scientific image processingDirect - Laplace transform inversion via the direct integration methodDirectSD - analysis and design of computer controlled systems with process-oriented modelsDMsuite - differentiation matrix suiteDMTTEQ - design and test time domain equalizer design methodsDrawFilt - drawing digital and analog filtersDSFWAV - spline interpolation with Dean wave solutionsDWT - discrete wavelet transformsEasyKrigEconometricsEEGLABEigTool - graphical tool for nonsymmetric eigenproblemsEMSC - separating light scattering and absorbance by extended multiplicative signal correctionEngineering VibrationFastICA - fixed-point algorithm for ICA and projection pursuitFDC - flight dynamics and controlFDtools - fractional delay filter designFlexICA - for independent components analysisFMBPC - fuzzy model-based predictive controlForWaRD - Fourier-wavelet regularized deconvolutionFracLab - fractal analysis for signal processingFSBOX - stepwise forward and backward selection of features using linear regressionGABLE - geometric algebra tutorialGAOT - genetic algorithm optimizationGarch - estimating and diagnosing heteroskedasticity in time series modelsGCE Data - managing, analyzing and displaying data and metadata stored using the GCE data structure specificationGCSV - growing cell structure visualizationGEMANOVA - fitting multilinear ANOVA modelsGenetic AlgorithmGeodetic - geodetic calculationsGHSOM - growing hierarchical self-organizing mapglmlab - general linear modelsGPIB - wrapper for GPIB library from National InstrumentGTM - generative topographic mapping, a model for density modeling and data visualizationGVF - gradient vector flow for finding 3-D object boundariesHFRadarmap - converts HF radar data from radial current vectors to total vectorsHFRC - importing, processing and manipulating HF radar dataHilbert - Hilbert transform by the rational eigenfunction expansion methodHMM - hidden Markov modelsHMMBOX - for hidden Markov modeling using maximum likelihood EMHUTear - auditory modelingICALAB - signal and image processing using ICA and higher order statisticsImputation - analysis of incomplete datasetsIPEM - perception based musical analysisJMatLink - Matlab Java classesKalman - Bayesian Kalman filterKalman Filter - filtering, smoothing and parameter estimation (using EM) for linear dynamical systemsKALMTOOL - state estimation of nonlinear systemsKautz - Kautz filter designKrigingLDestimate - estimation of scaling exponentsLDPC - low density parity check codesLISQ - wavelet lifting scheme on quincunx gridsLKER - Laguerre kernel estimation toolLMAM-OLMAM - Levenberg Marquardt with Adaptive Momentum algorithm for training feedforward neural networksLow-Field NMR - for exponential fitting, phase correction of quadrature data and slicingLPSVM - Newton method for LP support vector machine for machine learning problemsLSDPTOOL - robust control system design using the loop shaping design procedure LS-SVMlabLSVM - Lagrangian support vector machine for machine learning problemsLyngby - functional neuroimagingMARBOX - for multivariate autogressive modeling and cross-spectral estimationMatArray - analysis of microarray dataMatrix Computation - constructing test matrices, computing matrix factorizations, visualizing matrices, and direct search optimizationMCAT - Monte Carlo analysisMDP - Markov decision processesMESHPART - graph and mesh partioning methodsMILES - maximum likelihood fitting using ordinary least squares algorithmsMIMO - multidimensional code synthesisMissing - functions for handling missing data valuesM_Map - geographic mapping toolsMODCONS - multi-objective control system designMOEA - multi-objective evolutionary algorithmsMS - estimation of multiscaling exponentsMultiblock - analysis and regression on several data blocks simultaneouslyMultiscale Shape AnalysisMusic Analysis - feature extraction from raw audio signals for content-based music retrievalMWM - multifractal wavelet modelNetCDFNetlab - neural network algorithmsNiDAQ - data acquisition using the NiDAQ libraryNEDM - nonlinear economic dynamic modelsNMM - numerical methods in Matlab textNNCTRL - design and simulation of control systems based on neural networksNNSYSID - neural net based identification of nonlinear dynamic systemsNSVM - newton support vector machine for solving machine learning problemsNURBS - non-uniform rational B-splinesN-way - analysis of multiway data with multilinear modelsOpenFEM - finite element developmentPCNN - pulse coupled neural networksPeruna - signal processing and analysisPhiVis - probabilistic hierarchical interactive visualization, i.e. functions for visual analysis of multivariate continuous dataPlanar Manipulator - simulation of n-DOF planar manipulatorsPRTools - pattern recognitionpsignifit - testing hyptheses about psychometric functionsPSVM - proximal support vector machine for solving machine learning problemsPsychophysics - vision researchPyrTools - multi-scale image processingRBF - radial basis function neural networksRBN - simulation of synchronous and asynchronous random boolean networksReBEL - sigma-point Kalman filtersRegression - basic multivariate data analysis and regressionRegularization ToolsRegularization Tools XPRestore ToolsRobot - robotics functions, e.g. kinematics, dynamics and trajectory generationRobust Calibration - robust calibration in statsRRMT - rainfall-runoff modellingSAM - structure and motionSchwarz-Christoffel - computation of conformal maps to polygonally bounded regions SDH - smoothed data histogramSeaGrid - orthogonal grid makerSEA-MAT - oceanographic analysisSLS - sparse least squaresSolvOpt - solver for local optimization problemsSOM - self-organizing mapSOSTOOLS - solving sums of squares (SOS) optimization problemsSpatial and Geometric AnalysisSpatial RegressionSpatial StatisticsSpectral MethodsSPM - statistical parametric mappingSSVM - smooth support vector machine for solving machine learning problemsSTATBAG - for linear regression, feature selection, generation of data, and significance testingStatBox - statistical routinesStatistical Pattern Recognition - pattern recognition methodsStixbox - statisticsSVM - implements support vector machinesSVM ClassifierSymbolic Robot DynamicsTEMPLAR - wavelet-based template learning and pattern classificationTextClust - model-based document clusteringTextureSynth - analyzing and synthesizing visual texturesTfMin - continous 3-D minimum time orbit transfer around EarthTime-Frequency - analyzing non-stationary signals using time-frequency distributions Tree-Ring - tasks in tree-ring analysisTSA - uni- and multivariate, stationary and non-stationary time series analysisTSTOOL - nonlinear time series analysisT_Tide - harmonic analysis of tidesUTVtools - computing and modifying rank-revealing URV and UTV decompositions Uvi_Wave - wavelet analysisvarimax - orthogonal rotation of EOFsVBHMM - variation Bayesian hidden Markov modelsVBMFA - variational Bayesian mixtures of factor analyzersVMT - VRML Molecule Toolbox, for animating results from molecular dynamics experimentsVOICEBOXVRMLplot - generates interactive VRML 2.0 graphs and animationsVSVtools - computing and modifying symmetric rank-revealing decompositionsWAFO - wave analysis for fatique and oceanographyWarpTB - frequency-warped signal processingWAVEKIT - wavelet analysisWaveLab - wavelet analysisWeeks - Laplace transform inversion via the Weeks methodWetCDF - NetCDF interfaceWHMT - wavelet-domain hidden Markov tree modelsWInHD - Wavelet-based inverse halftoning via deconvolutionWSCT - weighted sequences clustering toolkitXMLTree - XML parserYAADA - analyze single particle mass spectrum dataZMAP - quantitative seismicity analysis。
分数时延滤波器设计
西安电子科技大学 关于论文使用授权的说明
本人完全了解西安电子科技大学有关保留和使用学位论文的规定，即：研究 生在校攻读学位期间论文工作的知识产权单位属西安电子科技大学。本人保证毕 业离校后，发表论文或使用论文工作成果时署名单位仍然为西安电子科技大学。 学校有权保留送交论文的复印件，允许查阅和借阅论文；学校可以公布论文的全 部或部分内容，可以允许采用影印、缩印或其它复制手段保存论文。同时本人保 证，毕业后结合学位论文研究课题再撰写的文章一律署名单位为西安电子科技大 学。 本人签名： 导师签名： 日期 日期
秉承学校严谨的学风和优良的科学道德，本人声明所呈交的论文是我个人在 导师指导下进行的研究工作及取得的研究成果。尽我所知，除了文中特别加以标 注和致谢中所罗列的内容以外，论文中不包含其他人已经发表或撰写过的研究成 果；也不包含为获得西安电子科技大学或其它教育机构的学位或证书而使用过的 材料。与我一同工作的同志对本研究所做的任何贡献均已在论文中做了明确的说 明并表示了谢意。 申请学位ቤተ መጻሕፍቲ ባይዱ文与资料若有不实之处，本人承担一切的法律责任。 本人签名： 日期
摘要
摘要
分数时延滤波器是一种时延的采样间隔为分数形式的数字滤波器。本文通过 设计合适的滤波器方案来逼近理想的分数时延滤波器的特性，由此实现输入信号 所期望的分数时延滤波器。 文中主要介绍两大类设计分数时延滤波器方法，第一类是通过 FIR 数字滤波 器的设计方法来实现，包括时延参数固定的最小二乘法、拉格朗日插值法、等波 纹法，以及时延参数可变的傅里叶变换法和 FARROW 结构法。另一类是通过全通 滤波器的设计方法来实现，包括时延参数固定的最小二乘法、最大平坦群延迟法、 等波纹法，以及时延参数可变的矩阵变换法和 FARROW 结构法。 在文章的最后，以宽带数字阵列雷达中的宽带阵列数字波束形成中需要用到 的分数时延滤波器为应用案例，尝试使用两种方法（多相结构法和 FARROW 结构 法）来实现其中的分数时延部分，并在结束时，对这两种方法做以比较和总结。 关键字：分数时延 等波纹 拉格朗日插值法 FARROW 结构 多相结构
非常经典 清华大学 李宇根 PLL讲义 Lecture12
Spring Semester, 2008PLL DESIGN AND CLOCK/FREQUENCY GENERATION (Lecture 12)Woogeun Rhee Institute of Microelectronics Tsinghua UniversityTerm Project• Design 645MHz fractional-N PLL circuit: - fref = 40MHz, fout = 645MHz with 50% duty cycle - Due date: June 24th40MHzfref(1) (2)645MHzPFD(3)CP(4)VCO(5)2(6)foutPLL BW: ~500kHz16/17 k-bit ACCUM2W. Rhee, Institute of Microelectronics, Tsinghua UniversityTerm Project (continued)• Do followings: 1. Design loop filter for ~500kHz PLL bandwidth. 2. Draw open-loop gain Bode plot based on LPF design from (a). 3. Plot node 3, 4 and check the lock time. 4. Plot node 1, 2 after PLL is fully settled. What is the amount of static phase offset? 5. Plot node 5, 6 for 10 VCO cycles (i.e. zoom-in plot). 6. Estimate the spur level based on VCO gain and waveform at node 3. 7. Verify (f) result by having FFT and measure spur level at VCO output in dBc. E1. Plot eye diagram of VCO output and measure jitter in time domain. (extra) E2. Run phase noise simulation of open-loop VCO and calculate closed-loop RJ. (extra) E3. Calculate closed-loop RJ by defining approximated noise bandwidth. (extra) E4. Tell whether DJ or RJ is dominant. (extra) • Note: Ideal blocks allowed for PFD & LPF design3W. Rhee, Institute of Microelectronics, Tsinghua UniversityV. Applications 3. Clock Multiplier Unit (CMU)4W. Rhee, Institute of Microelectronics, Tsinghua UniversityCMU Design Considerations• Similar to RF frequency synthesizer - Use of frequency divider and PFD/CP - Trade-off between noise and spur • Different from RF frequency synthesizer - Less stringent lock-in time - Ultimately interested in pk-pk jitter. - Noisier supply voltage - Noisier reference clock - Lower supply voltage - Mostly in digital CMOS process - Ring VCO and on-chip LPF preferred.5W. Rhee, Institute of Microelectronics, Tsinghua UniversityJitter• Absolute jitter (long-term jitter) - Phase error w.r.t. ideal referenceΔTabs ,rms = lim1 2 ΔT12 + ΔT22 + ⋅ ⋅ ⋅ + ΔTN N →∞ N• Cycle-to-cycle jitter (short-term jitter) - No need for referenceΔTcc ,rms ≈ lim1 (T2 − T1 )2 + (T3 − T2 )2 + ⋅ ⋅ ⋅ + (TN − TN −1 )2 N →∞ N• Period jitter - For PLL, period jitter = absolute jitter.ΔTp ,rms = lim1 (T − T1 )2 + (T − T2 )2 + ⋅ ⋅ ⋅ + (T − TN −1 )2 N →∞ N*Note:Periodic jitter (PJ) is often considered DJ by sinusoidal modulation, which is different from period jitter.W. Rhee, Institute of Microelectronics, Tsinghua University6Total Jitter (TJ)RJpk-pk (14*σ)• Total jitter (TJpp) - RJpp + DJpp = 14 x RJrms + DJpp • Random jitter (RJ) - Non-systematic jitter - Gaussian distribution • Deterministic jitter (DJ) - Systematic jitter - Coupling and ISI - Duty cycle distortionDJDJ dominant (modulation)RJ dominant (noise)Pspurfo7W. Rhee, Institute of Microelectronics, Tsinghua UniversityRandom Jitter (RJ)Bathtub Curve• For BER = 10-12, RJpp = 14 x RJrmsRef: “Jitter Fundamentals,” Wavecrest Company8W. Rhee, Institute of Microelectronics, Tsinghua UniversityRJ and Noise Integration BandwidthfoCDR tracking BWPDLPFCDRN• CDR tracking BW should be considered for TXPLL design. - SONET: 50kHz – 80MHz - Typically (Baud Rate) / 1667 – (Baud Rate) / 29W. Rhee, Institute of Microelectronics, Tsinghua UniversitySupply Noise EffectfoCDR tracking BWPDLPFCDRN10W. Rhee, Institute of Microelectronics, Tsinghua UniversityJSSC’96, von Kaenel et al. Supply Noise ConsiderationSupply w/o NoiseSupply w/t Noise(f 3dBLess power but needs more careful design for 50% duty cycle.Cascaded PLLsParallel PLLsISSCC’03, Wong et al.Cascaded PLLsV. Applications3. Clock Multiplier Unit (CMU)A. Uniform BW control for PCIe2B. ΔΣPLL for digital clock generationC. S-S clocking for EMI reductionInside PCCurrent ComingFB-DIMM•DDR2 DRAM + high-speed serial linkÆPoint-to-point serial link communication •Overcomes trade-off between speed and capacity.[Li, ITC’04], [PCI-SIG]s o 123H s H s e H s H s −Δτ=−⋅()[()()]()H 1(s)H 3(s)H 2(s)ΔτLC VCORing VCO[Noguchi, ISSCC’02][Herzel, JSSC’03][Moon, JSSC’04][Williams, CICC’04]Dual-Path VCOsTimeTimeVarious Coarse-Tuning Gains(with BW FINE = 1)Various Coarse-Tuning Bandwidths(with BW FINE = 1)(CppSim tool from M.I.T. used for simulation)PLL Behavioral Simulation(<80kHz)(10MHz)VDDINBINBIASOUT OUTBR1R2Narrowbanding (for coarse tuning)4th -pole of PLL (for fine tuning)Resistor noise contribution to PLLH(f)fF RCF BWLinear Amplifier and Noise ConsiderationPhase Noise PerformancesMeasured RJ VariationMeasured VCO Tuning CurvePSRR PerformanceV. Applications3. Clock Multiplier Unit (CMU)A. Uniform BW control for PCIe2B. ΔΣPLL for digital clock generationC. S-S clocking for EMI reductionFractional-N PLL for Wireline Applications?Flexible Frequency Planning with ΔΣPLL•Conventional PLL makes it difficult to accommodate various reference clock frequencies.Digital Clock Generation with <1ppm Resolution•PLL with ring VCO needs wide bandwidth to suppress VCO noise.ÆLow f ref /f bw ratio makes it difficult to implement ΔΣfractional-N PLL.ÆSuffer from cycle-to-cycle jitter problem due to quantization noise.Fractional-N PLL for Digital SystemL f ) d B c /H z )Basic ConceptsEquivalent Discrete-Time Model Frequency ResponseL ) B c H zBehavioral Simulation Results500MHz Output Spectrum(Fref= 14.318MHz, N=37.15603)VCO Control Voltage•FIR-embedded frequency divider reduces output cycle-to-cycle jitter.ISCAS’07, Chi et al.Measured Output SpectraV. Applications3. Clock Multiplier Unit (CMU)A. Uniform BW control for PCIe2B. ΔΣPLL for digital clock generationC. S-S clocking for EMI reductionElectromagnetic Interference (EMI)•Radiation emission is strictly regulated by FCC.•Can be reduced by shielded cables but expensive and bulky.ÆHow about modulating clock to reduce peak power?Modulation Profile Clock SpectrumCarrier(w/o modulation)Spread Spectrum ClockingJSSC’03, Chang et al.By Voltage ModulationBy Divider Modulation By ΔΣModulation ISSCC’99, Li et al.ISSCC’05, Lee et al.。
基于multisim和filtersolution的巴特沃斯滤波器的设计与仿真
基于m u ltisi m和filter so lu ti on的巴特沃斯滤波器的设计与仿真广东机电职业技术学院计算机系 程 光[摘 要]巴特沃斯滤波器因为具有最平坦的通带幅频特性,故广泛被电子设计者所应用,但其低阶的滤波器通带边界下降较慢。
高阶滤波电路通常都是以1阶和2阶滤波器的设计为基础,为此,本文从基础的2阶巴特沃斯低通滤波器的设计入手,详细介绍设计过程,然后在m ultisi m下给予验证,最后用filter so luti on设计高阶的,通带边界下降更快的低通滤波器。
[关键词]巴特沃斯滤波器 2阶 低通 m ultisi m filter so luti on(上接第303页)是大都市,抢占大市场。
为此,作为地方中小企业应避免与这些强劲品牌产生正面冲突,不要在本已十分拥挤的都市道路上步履蹒跚,而应在潜在的广大农村市场上纵横驰骋,找出知名品牌无力顾及或仍未开发的市场空间,找准切入点,推出自己的品牌,在小市场中发展和壮大自己。
在市场竞争中,地方中小企业应注意保持低调务实的姿态,不要过多张扬自己的行动,以免惊动主导品牌。
3、搞好产品品牌的设计工作中小企业在进行产品品牌设计过程中,首先要突出产品品牌的个性。
品牌个性是品牌形象的核心,是消费者认知品牌的尺度和重心。
是品牌形象中最能体现差异、最活跃激进的部分。
为使品牌个性突出、鲜明,必须整合各种因素,使之加强消费者对品牌个性的认知,与消费者产生共鸣。
如:奔驰具有“自负、富有”的个性,百事可乐具有“年轻、活泼、刺激”的个性。
其次,要给产品命好名。
要使企业产品品牌的名字简洁醒目,易读易记;品牌构思巧妙,有所暗示;色彩美丽而富有个性;同时要尊重习俗、符合法律。
第三,要设计产品包装。
在设计产品包装时,充分考虑安全、便于携带、美观大方、色彩搭配协调等。
4、做好产品品牌的宣传和推广工作中小企业在进行产品品牌的宣传和推广工作过程中,切不能照搬大型企业的方法和模式,斥巨资大搞广告宣传。
Filter solution 使用说明
Filter solution 使用说明Albus 2011.12.211.Filter solution软件介绍：Filter solution是由Nuhertz Technologies,LLC公司开发的一款滤波器设计和分析软件，能够提供无源、有源和数字滤波设计类型，可给出所设计滤波器的传递函数、零极点以及幅频、相频、群时延等特性。
通过调整参数，可以获得实际工程需要的滤波器。
另外，数字滤波器还可以生成C语言程序。
是一款非常实用的工具。
2.使用：下面以设计一个截止频率为300kHz的滤波器为例，介绍一下该软件的使用：设计来源：xx项目中关于低通滤波器部分设计的需求。
源文件见目录中“低通300K..ftr”文件。
本系统的设计中用到的软件版本为Filter solution zvan10.0，软件界面如下图所示：（一）参数设计：如上图所示，在软件左侧一栏选择所设计的滤波器的模型，现选择Butterworth模型；中间部分选择设计的滤波器的阶数和截止频率，现输入3阶，截止频率输入为300kHz；下面几栏分别选择滤波器的类型、仿真的频率和时间范围等。
右侧一栏分别包括滤波器的传输特性、模型补充选项、放大倍数以及负载大小的选择。
（二）电路图的生成：输入滤波器的参数之后，点击“Circuit”，生成电路图如下图所示：（三）滤波器功能仿真：在Filter solution主界面点击“Frequence Response”,生成该电路的幅频响应曲线，如下图所示：由幅频响应图像可知，当幅度衰减3dB时对应的频率为300kHz，达到了设计的目标。
上述各参数的设置，可以根据实际运用来选择，软件比较小巧实用，设置起来比较方便。
ECE_94
ORIGINAL :UNITED NATIONS of March 20, 1995E/ECE/324 )Rev.1/Add.93/Amend.4E/ECE/TRANS/505 )April 1, 2003STATUS OF UNITED NATIONS REGULATIONECE 94UNIFORM PROVISIONS CONCERNING THE APPROVAL OF:VEHICLES WITH REGARD TO THE PROTECTION OF THEOCCUPANTS IN THE EVENT OF A FRONTAL COLLISIONIncorporating:00 series of amendments Date of Entry into Force: 01.10.95 Supplement 1 to the 00 series of amendments Date of Entry into Force: 12.08.96 01 series of amendments Date of Entry into Force: 12.08.98 Supplement 1 to the 01 series of amendments Date of Entry into Force: 21.02.02 Supplement 2 to the 01 series of amendments Date of Entry into Force: 31.01.03 Corr. 1 to the 01 series of amendments Date of Entry into Force: 26.06.02ORIGINAL :UNITED NATIONS of March 20, 1995 E/ECE/324)E/ECE/TRANS/505 )Rev.1/Add.93/Amend.4April 1, 2003TITLE:Frontal Collision - ISSUE:4 Regulation No. 94Protection Apr/2003PAGE: IUNITED NATIONS AGREEMENTCONCERNING THE ADOPTION OF UNIFORM TECHNICAL PRESCRIPTIONS FOR WHEELED VEHICLES, EQUIPMENT AND PARTS WHICH CAN BE FITTED AND/OR BE USED ON WHEELED VEHICLES AND THE CONDITIONS FOR RECIPROCAL RECOGNITION OFAPPROVALS GRANTED ON THE BASIS OF THESE PRESCRIPTIONS (*)Revision 2, including the amendments which entered into force on October 16, 1995)Addendum 93: Regulation No. 94Amendment 4Supplement 2to the 01 series of amendments – Date of entry into force: January 31, 2003UNIFORM PROVISIONS CONCERNING THE APPROVAL OF VEHICLES WITH REGARD TO THEPROTECTION OF THE OCCUPANTS IN THE EVENT OF A FRONTAL COLLISION(*)Former title of the Agreement:Agreement Concerning the Adoption of Uniform Conditions of Approval and Reciprocal Recognition of Approval for Motor Vehicle Equipment and Parts, done at Geneva on March 20, 1958.ORIGINAL :UNITED NATIONS of March 20, 1995Regulation No. 94UNIFORM PROVISIONS CONCERNING THE APPROVAL OF VEHICLES WITH REGARD TO THE PROTECTION OF THE OCCUPANTS IN THE EVENT OF A FRONTAL COLLISION CONTENTSREGULATION1. Scope2. Definitions3. Application for approval4. Approval5. Specifications6. Instructions for users of vehicles equipped with airbags7. Modification and Extension of approval of the vehicle type8. Conformity of production9. Penalties for non-conformity of production10. Production definitely discontinued11. Transitional provisions12. Names and addresses of technical services responsible for conducting approval tests, and ofadministrative departmentsANNEXESAnnex 1 - Communication concerning the approval or extension or refusal or withdrawal of approval or production definitely discontinued of a vehicle type with regard to the protection of theoccupants in the event of a frontal collision, pursuant to Regulation No. 94Annex 2 - Arrangements of the approval markAnnex 3 - Test procedureAnnex 4 - Determination of performance criteriaAnnex 5 - Arrangement and installation of dummies and adjustment of restraint systemsTITLE:Frontal Collision - ISSUE:1 Regulation No. 94 Protection Jan/1999PAGE: IIORIGINAL :UNITED NATIONS of March 20, 1995Regulation No. 94Annex 6 - Procedure for determining the "H" point and the actual torso angle for seating positions in motor vehiclesAppendix 1 - Description of the three-dimensional "H" point machineAppendix 2 - Three-dimensional reference systemAppendix 3 - Reference data concerning seating positionsAnnex 7 - Test procedure with trolleyAppendix - Equivalence curve - Tolerance band for curve _V = f (t)Annex 8 - Technique of measurement in measurement tests: instrumentationAnnex 9 - Definition of the deformable barrierAnnex 10 - Certification procedure for the dummy lower leg and foot.TITLE:Frontal Collision - ISSUE:1 Regulation No. 94 Protection Jan/1999PAGE: IIIORIGINAL :UNITED NATIONS of March 20, 1995TITLE:Frontal Collision - ISSUE:1 Regulation No. 94Protection Jan/1999PAGE: 1Regulation No. 941.SCOPE1.1.This regulation applies to power-driven vehicles of Category M 1(1)of a total permissible mass not exceeding 2.5 tonnes; heavier vehicles may be approved at the request of the manufacturer;1.2.It shall apply at the request of the manufacturer for the approval of a vehicle type with regard to the protection of the occupants of the front outboard seats in the event of a frontal collision. 2.DEFINITIONSFor the purposes of this Regulation:2.1."Protective system" means interior fittings and devices intended to restrain the occupants and contribute towards ensuring compliance with the requirements set out in Paragraph 5 below;2.2."Type of protective system" means a category of protective devices which do not differ in such essential respects as: Their technology; Their geometry;Their constituent materials;2.3."Vehicle width" means the distance between two planes parallel to the longitudinal median plane (of the vehicle) and touching the vehicle on either side of the said plane but excluding the rear-view mirrors, side marker lamps, tyre pressure indicators, direction indicator lamps, position lamps, flexible mud-guards and the deflected part of the tyre side-walls immediately above the point of contact with the ground;2.4. "Overlap" means the percentage of the vehicle width directly in line with the barrier face; 2.5. "Deformable barrier face" means a crushable section mounted on the front of a rigid block;2.6."Vehicle type" means a category of power-driven vehicles which do not differ in such essential respects as:2.6.1. The length and width of the vehicle, in so far as they have a negative effect on the results of the impact test prescribed in this Regulation,2.6.2.The structure, dimensions, lines and materials of the part of the vehicle forward of the transverse plane through the "R" point of the driver's seat, in so far as they have a negative effect on the results of the impact test prescribed in this Regulation,(1)As defined in the Consolidated Resolution on the Construction of Vehicles (R.E.3), Annex 7 (document TRANS/SC1/WP29/78/Amend.3), i.e., motor vehicles used for the carriage of passengers and comprising not more than eight seats in addition to the driver's seat.ORIGINAL :UNITED NATIONS of March 20, 19952.6.3.The lines and inside dimensions of the passenger compartment and the type of protectivesystem, in so far as they have a negative effect on the results of the impact test prescribedin this Regulation,2.6.4.The siting (front, rear or centre) and the orientation (transversal or longitudinal) of theengine,2.6.5.The unladen mass, in so far as there is a negative effect on the result of the impact testprescribed in this Regulation,2.6.6.The optional arrangements or fittings provided by the manufacturer, in so far as they have anegative effect on the result of the impact test prescribed in this Regulation,2.7."Passenger compartment"means the space for occupant accommodation, bounded bythe roof, floor, side walls, doors, outside glazing and front bulkhead and the plane of the rearcompartment bulkhead or the plane of the rear-seat back support;2.8."R point" means a reference point defined for each seat by the manufacturer in relation thevehicle's structure, as indicated in Annex 6;2.9."H point"means a reference point determined for each seat by the testing serviceresponsible for approval, in accordance with the procedure described in Annex 6;2.10."Unladen kerb mass"means the mass of the vehicle in running order, unoccupied andunladen but complete with fuel, coolant , lubricant, tools and spare wheel (if these areprovided as standard equipment by the vehicle manufacturer).2.11."Airbag"means a device installed to supplement safety belts and restraint systems inpower-driven vehicles, i.e. systems which, in the event of a severe impact affecting thevehicle, automatically deploy a flexible structure intended to limit, by compression of the gascontained within it, the gravity of the contacts of one or more parts of the body of anoccupant of the vehicle with the interior of the passenger compartment.2.12."Passenger airbag"means an airbag assembly intended to protect occupant(s) in seatsother than the driver's in the event of a frontal collision.2.13."Child restraint"means an arrangement of components which may comprise acombination of straps or flexible components with a securing buckle, adjusting devices,attachments, and in some cases a supplementary chair and/or an impact shield, capable ofbeing anchored to a power driven vehicle. It is so designed as to diminish the risk of injuryto the wearer, in the event of a collision or of abrupt deceleration of the vehicle by limitingthe mobility of the wearer's body.2.14."Rearward-facing" means facing in the direction opposite to the normal direction of travelof the vehicle.TITLE:Frontal Collision - ISSUE:1 Regulation No. 94 Protection Jan/1999PAGE: 2ORIGINAL :UNITED NATIONS of March 20, 19953.APPLICATION FOR APPROVAL3.1.The application for approval of a vehicle type with regard to the protection of the occupantsof the front seats in the event of a frontal collision shall be submitted by the vehiclemanufacturer or by his duly accredited representative.3.2.It shall be accompanied by the undermentioned documents in triplicate and followingparticulars;3.2.1. A detailed description of the vehicle type with respect to its structure, dimensions, lines andconstituent materials;3.2.2.Photographs, and/or diagrams and drawings of the vehicle showing the vehicle type in front,side and rear elevation and design details of the forward part of the structure;3.2.3.Particulars of the vehicle's unladen kerb mass;3.2.4.The lines and inside dimensions of the passenger compartment;3.2.5. A description of the interior fittings and protective systems installed in the vehicle.3.3.The applicant for approval shall be entitled to present any data and results of tests carriedout which make it possible to establish that compliance with the requirements can beachieved with a sufficient degree of confidence.3.4. A vehicle which is representative of the type to be approved shall be submitted to thetechnical service responsible for conducting the approval tests.3.4.1. A vehicle not comprising all the components proper to the type may be accepted for testprovided that it can be shown that the absence of the components omitted has nodetrimental effect on the results of the test in so far as the requirements of this Regulationare concerned.3.4.2.It shall be the responsibility of the applicant for approval to show that the application ofParagraph 3.4.1. is compatible with compliance with the requirements of this Regulation. TITLE:Frontal Collision - ISSUE:1 Regulation No. 94 Protection Jan/1999PAGE: 3ORIGINAL :UNITED NATIONS of March 20, 1995 TITLE:Frontal Collision - ISSUE:3 Regulation No. 94Protection Apr/2003PAGE: 44.APPROVAL4.1. If the vehicle type submitted for approval pursuant to this Regulation meets the requirements of this Regulation , approval of that vehicle type shall be granted.4.1.1. The technical service appointed in accordance with Paragraph 10 below shall check whether the required conditions have been satisfied.4.1.2.In case of doubt, account shall be taken, when verifying the conformity of the vehicle to the requirements of this Regulation, of any data or test results provided by the manufacturer which can be taken into consideration in validating the approval test carried out by the technical service.4.2.An approval number shall be assigned to each type approved. Its first two digits (at present 01 corresponding to the 01 series of amendments), shall indicate the series of amendments incorporating the most recent major technical amendments made to the Regulation at the time of issue of the approval. The same Contracting Party may not assign the same approval number to another vehicle type.4.3.Notice of approval or of refusal of approval of a vehicle type pursuant to this Regulation shall be communicated by the Parties to the Agreement which apply this Regulation by means of a form conforming to the model in Annex 1 to this Regulation and photographs and/or diagrams and drawings supplied by the applicant for approval, in a format not exceeding A4 (210 X 297 mm) or folded to that format and on an appropriate scale.4.4.There shall be affixed, conspicuously and in a readily accessible place specified on the approval form, to every vehicle conforming to a vehicle type approved under this Regulation, an international approval mark consisting of:4.4.1. A circle surrounding the Letter "E" followed by the distinguishing number of the country which has granted approval (1)4.4.2.The number of this Regulation, followed by the Letter "R", a dash and the approval number, to the right of the circle prescribed in Paragraph 4.4.1.(1)1 for Germany,2 for France,3 for Italy,4 for the Netherlands,5 for Sweden,6 for Belgium,7 for Hungary,8 for the Czech Republic,9 for Spain, 10 for Yugoslavia, 11 for the United Kingdom, 12 for Austria, 13 for Luxembourg, 14 for Switzerland, 15 (vacant), 16 for Norway, 17 for Finland, 18 for Denmark, 19 for Romania, 20 for Poland, 21 for Portugal, 22 for the Russian Federation, 23 for Greece, 24 for Ireland, 25 for Croatia, 26 for Slovenia, 27 for Slovakia, 28 for Belarus, 29 for Estonia, 30 (vacant), 31 for Bosnia and Herzegovina, 32 for Latvia, 33 (vacant), 34 for Bulgaria, 35 (vacant), 36 for Lithuania,37 for Turkey, 38 (vacant), 39 for Azerbaijan, 40 for The former Yugoslav Republic of Macedonia, 41 (vacant), 42 for the European Community (Approvals are granted by its Member States using their respective ECE symbol), 43 for Japan, 44 (vacant), 45 for Australia, 46 for Ukraine, 47 for South Africa and 48 for New Zealand. Subsequent numbers shall be assigned to other countries in the chronological order in which they ratify to the Agreement concerning the Adoption of Uniform Technical Prescriptions for Wheeled Vehicles, Equipment and Parts which can be Fitted and/or be Used on Wheeled Vehicles and the Conditions for Reciprocal Recognition of Approvals Granted on the Basis of these Prescriptions, for Motor Vehicle Equipment and Parts, or in which they accede to that Agreement, and the numbers thus assigned shall be communicated by the Secretary-General of the United Nations to the Contracting Parties to the Agreement.ORIGINAL :UNITED NATIONS of March 20, 19954.5.If the vehicle conforms to a vehicle type approved, under one or more other Regulationsannexed to the Agreement, in the country which has granted approval under thisRegulation, the symbol prescribed in Paragraph 4.4.1. need not be repeated; in such a casethe Regulation and approval numbers and the additional symbols of all the Regulationsunder which approval has been granted in the country which has granted approval underthis Regulation shall be placed in vertical columns to the right of the symbol prescribed inParagraph 4.4.1.4.6.The approval mark shall be clearly legible and be indelible.4.7.The approval mark shall be placed close to or on the vehicle data plate affixed by themanufacturer.4.8.Annex 2 to this Regulation gives examples of approval marks.5.SPECIFICATIONS5.1.General specifications applicable to all tests5.1.1.The "H" point for each seat shall be determined in accordance with the procedure describedin Annex 6.5.1.2.When the protective system for the front seating positions includes belts, the beltcomponents shall meet the requirements of Regulation No. 16.5.1.3.Seating positions where a dummy is installed and the protective system includes belts, shallbe provided with anchorage points conforming to Regulation No. 14.5.2.SpecificationsThe test of the vehicle carried out in accordance with the method described in Annex 3 shallbe considered satisfactory if all the conditions set out in Paragraphs 5.2.1. to 5.2.6. beloware all satisfied at the same time.5.2.1.The performance criteria recorded, in accordance with Annex 8, on the dummies in the frontoutboard seats shall meet the following conditions:5.2.1.1. The head performance criterion (HPC) shall not exceed 1000 and the resultant headacceleration shall not exceed 80 g for more than 3 ms. The latter shall be calculatedcumulatively, excluding rebound movement of the head;TITLE:Frontal Collision - ISSUE:1 Regulation No. 94 Protection Jan/1999PAGE: 5ORIGINAL :UNITED NATIONS of March 20, 1995 TITLE:Frontal Collision - ISSUE:1 Regulation No. 94Protection Jan/1999PAGE: 65.2.1.2.The neck injury criteria (NIC) shall not exceed the values shown in Figures 1 and 2(1);Figure 1Neck Tension CriterionFigure 2 Neck Shear Criterion(1)Until October 1, 1998, the values obtained for the neck shall not be pass/fail criteria for the purposes of granting approval.The results obtained shall be recorded in the test report and be collected by the approval authority. After this date, the values specified in this paragraph shall apply as pass/fail criteria unless or until alternative values are adopted.ORIGINAL :UNITED NATIONS of March 20, 1995 TITLE:Frontal Collision - ISSUE:1 Regulation No. 94Protection Jan/1999PAGE: 75.2.1.3. The neck bending moment about the y axis shall not exceed 57 Nm in extension (1);5.2.1.4. The thorax compression criterion (ThCC) shall not exceed 50 mm; 5.2.1.5. The viscous criterion (V * C) for the thorax shall not exceed 1,0 m/s;5.2.1.6.The femur force criterion (FFC) shall not exceed the force-time performance criterion shownin Figure 3;Figure 3Femur Force Criterion5.2.1.7. The tibia compression force criterion (TCFC) shall not exceed 8 kN;5.2.1.8. The tibia index (TI), measured at the top and bottom of each tibia, shall not exceed 1,3 at either location;5.2.1.9. The movement of the sliding knee joints shall not exceed 15 mm.5.2.2.Residual steering wheel displacement, measured at the centre of the steering wheel hub, shall not exceed 80 mm in the upwards vertical direction and 100 mm in the rearward horizontal direction.(1)Until October 1, 1998, the values obtained for the neck shall not be pass/fail criteria for the purposes of granting approval.The results obtained shall be recorded in the test report and be collected by the approval authority. After this date, the values specified in this paragraph shall apply as pass/fail criteria unless or until alternative values are adopted.ORIGINAL :UNITED NATIONS of March 20, 19955.2.3.During the test no door shall open;5.2.4.During the test no locking of the locking systems of the front doors shall occur;5.2.5.After the impact, it shall be possible, without the use of tools, except for those necessary tosupport the weight of the dummy:5.2.5.1. To open at least one door, if there is one, per row of seats and, where there is no such door,to move the seats or tilt their backrests as necessary to allow the evacuation of all theoccupants; this is, however, only applicable to vehicles having a roof of rigid construction; 5.2.5.2. To release the dummies from their restraint system which, if locked, shall be capable ofbeing released by a maximum force of 60 N on the centre of the release control;5.2.5.3. To remove the dummies from the vehicle without adjustment of the seats.5.2.6.In the case of a vehicle propelled by liquid fuel, no more than slight leakage of liquid fromthe fuel feed installation shall occur on collision;5.2.7.If there is continuous leakage of liquid from the fuel-feed installation after the collision, therate of leakage shall not exceed 30 g/min; if the liquid from the fuel-feed system mixes withliquids from the other systems and the various liquids cannot easily be separated andidentified, all the liquids collected shall be taken into account in evaluating the continuousleakage.6.INSTRUCTIONS FOR USERS OF VEHICLES EQUIPPED WITH AIRBAGS6.1.The vehicles shall carry information to the effect that it is equipped with airbags for seats. 6.1.1.For a vehicle fitted with an airbag assembly intended to protect the driver, this informationshall consist of the inscription "AIRBAG" located in the interior of the circumference of thesteering wheel; this inscription shall be durably affixed and easily visible.6.1.2.For a vehicle fitted with a passenger airbag intended to protect occupants other than thedriver, this information shall consist of the warning label described in Paragraph 6.2. below.6.2. A vehicle fitted with one or more passenger frontal protection airbags shall carry informationabout the extreme hazard associated with the use of rearward-facing child restraints onseats equipped with airbag assemblies.TITLE:Frontal Collision - ISSUE:2 Regulation No. 94 Protection Apr/2003PAGE: 8ORIGINAL :UNITED NATIONS of March 20, 1995 TITLE:Frontal Collision - ISSUE:2 Regulation No. 94Protection Apr/2003PAGE: 96.2.1.As a minimum, this information shall consist of a label containing a pictogram and text warningas indicated below.The overall dimensions shall be 120 x 60 mm or the equivalent area, as a minimum. The label shown above may be adapted in such a way that the layout differs from the example above; however, the text content shall meet the above prescriptions.6.2.2.At the time of type approval, the label shall be in at least one of the languages of the Contracting Party where the application for approval is submitted. The manufacturer shall declare his responsibility for ensuring the warning is provided at least in one of the languages of the country in which the vehicle is to be sold.6.2.3.In the case of a frontal protection airbag on the front passenger seat, the warning shall be durably affixed to each face of the passenger front sun visor in such a position that at least one warning on the sun visor is visible at all times, irrespective of the position of the sun visor. Alternatively, one warning shall be on the visible face of the stowed sun visor and a second warning shall be on the roof behind the visor, so, at least one warning is visible at all times. The text size must allow the label to be easily read by a normal sighted user seated on the seat concerned.In the case of a frontal protection airbag for other seats in the vehicle, the warning must be directly ahead of the relevant seat, and clearly visible at all times to someone installing a rear-facing child restraint on that seat. The text size must allow the label to be easily read by a normal sighted user seated on the seat concerned.This requirement does not apply to those seats equipped with a device which automatically deactivates the frontal protection airbag assembly when any rearward-facing child restraint is installed.ORIGINAL :UNITED NATIONS of March 20, 1995 TITLE:Frontal Collision - ISSUE:2 Regulation No. 94Protection Apr/2003PAGE: 106.2.4.Detailed information, making reference to the warning, shall be contained in the owner's manual of the vehicle; as a minimum the following text in the official languages of the country where the vehicle is to be registered, must include:"Do not use a rearward facing child restraint on a seat protected by an airbag in front of it!"The text shall be accompanied by an illustration of the warning to be found in the vehicle.7.MODIFICATION AND EXTENSION OF APPROVAL OF THE VEHICLE TYPE7.1.Any modification affecting the structure, the number of seats, the interior trim or fittings, or the position of the vehicle controls or of mechanical parts which might affect the energy-absorption capability of the front of the vehicle shall be brought to the notice of the administrative department granting approval. The department may then either:7.1.1. Consider that the modifications made are unlikely to have an appreciable adverse effect and that in any case the vehicle still complies with the requirements; or7.1.2. Require the technical service responsible for conducting the tests to carry out a further test, among those described below, according to the nature of the modifications;7.1.2.1.Any modification of the vehicle affecting the general form of the structure of the vehicle and/or any increase in mass greater than 8% which in the judgement of the authority would have a marked influence on the results of the tests shall require a repetition of the test as described in Annex 3;7.1.2.2.If the modifications concern only the interior fittings, if the mass does not differ by more than 8 percent and if the number of front seats initially provided in the vehicle remains the same, the following shall be carried out:7.1.2.2.1. A simplified test as provided for in Annex 7 and/or,7.1.2.2.2. A partial test as defined by the technical service in relation to the modifications made. 7.2.Confirmation or refusal of approval, specifying the alterations, shall be communicated by the procedure specified in Paragraph 4.3. above to the Parties to the Agreement which apply this Regulation.7.3.The competent authority issuing the extension of approval shall assign a series number for such an extension and inform thereof the other Parties to the 1958 Agreement applying this Regulation by means of communication form conforming to the model in Annex 1 to this Regulation.8.CONFORMITY OF PRODUCTIONThe conformity of production procedures shall comply with those set out in the Agreement, Appendix 2 (E/ECE/324-E/ECE/TRANS/505/Rev.2) with the following requirements: 8.1.Every vehicle approved under this Regulation shall conform to the vehicle type approved, as regards features contributing to the protection of the occupants of the vehicle in the event of a frontal collision.8.2. The holder of the approval shall ensure that for each type of vehicle at least the tests concerning the taking of measurements are carried out;8.3.The authority which has granted type approval may at any time verify the conformity control methods applied in each production facility. The normal frequency of these verifications shall be once every two years.ORIGINAL :UNITED NATIONS of March 20, 19959.PENALTIES FOR NON-CONFORMITY OF PRODUCTION9.1.The approval granted in respect of a vehicle type pursuant to this Regulation may bewithdrawn if the requirement laid down in Paragraph 8.1. above is not complied with or if thevehicle or vehicles selected have failed to pass the checks prescribed in Paragraph 8.2.above.9.2.If a Contracting Party to the Agreement applying this Regulation withdraws an approval ithas previously granted, it shall forthwith so notify the other Contracting Parties applying thisRegulation, by means of a communication form conforming to the model in Annex 1 to theRegulation.10.PRODUCTION DEFINITELY DISCONTINUEDIf the holder of the approval completely ceases to manufacture the type of vehicle approvedin accordance with the Regulation, he shall so inform the authority which granted theapproval. Upon receiving the relevant communication that authority shall inform thereof theother Parties to the 1958 Agreement applying this Regulation by means of a communicationform conforming to the model in Annex 1 to this Regulation.11.TRANSITIONAL PROVISION11.1.As from the official date of entry into force of Supplement 1 to the 01 series of amendments,no Contracting Party applying this Regulation shall refuse to grant ECE approval under thisRegulation as amended by Supplement 1 to the 01 series of amendments.11.2.As from October 1, 2002Contracting Parties applying this Regulation shall grantECE approvals only to those types of vehicles which comply with the requirements of thisRegulation as amended by Supplement 1 to the 01 series of amendments.11.3.As from October 1, 2003 Contracting Parties applying this Regulation may refuse firstnational registration (first entry into service) of vehicles which do not meet the requirementsof this Regulation as amended by the 01 series of amendments.S AND ADDRESSES OF TECHNICAL SERVICES RESPONSIBLE FORCONDUCTING APPROVAL TESTS, AND OF ADMINISTRATIVE DEPARTMENTSThe Contracting Parties to the Agreement applying this Regulation shall communicate to theUnited Nations secretariat the names and addresses of the technical services responsiblefor conducting approval tests, of manufacturers authorised to carry out tests and of theadministrative departments which grant approval and to which forms certifying approval orrefusal or withdrawal of approval, issued in other countries, are to be sent.TITLE:Frontal Collision - ISSUE:2 Regulation No. 94 Protection June/2002PAGE: 11。
分数分频锁相环
分数分频锁相环分数分频锁相环（Fractional-N phase-locked loop，简称Fractional-N PLL）是一种基于数字信号处理技术的锁相环电路。
在现代通信系统中，由于需要对高速数字信号进行精确且可靠的重构和时钟提取，因此Fractional-N PLL得到了广泛的应用。
Fractional-N PLL通常由数字控制电路（Digital Control）和本体振荡电路（Oscillator）两部分组成。
其中Osclliator用于生成系统基准时钟信号，而Digital Control则通过对振荡电路频率和相位的数码调制，实现了系统时钟的同步和重构。
与传统锁相环相比，Fractional-N PLL的特点是其能够在倍数分频的基础上，再通过分数分频的技术实现更精确的频率调制。
具体地，Fractional-N PLL可以通过改变具有不同加权系数的信号频率来精确调整输出时钟频率，并实现非整数倍频。
Fractional-N PLL具有以下优点：1. 高精度：通过分数分频技术，Fractional-N PLL可以实现非整数倍频，因此对于一些要求高精度时序控制的应用，如无线通信和高速信号处理，Fractional-N PLL是一个理想的选择。
2. 运算速度快：由于Fractional-N PLL采用了数字信号处理技术，因此其运算速度比模拟锁相环更快，而且灵活性也更大。
3. 功耗低：由于Fractional-N PLL采用了数字控制技术，其电路结构较为简单，从而实现了较低的功耗。
以上优点使得Fractional-N PLL在许多领域被广泛应用，例如数字电视、ADSL调制解调器、无线通信系统等。
Fractional-N PLL的实现过程中需要注意以下几点：1. 计算加权系数时应考虑到系统的误差和抖动等因素，以保证调制精度。
2. 数字控制器的设计应具有较高的控制精度和稳定性，以确保系统时钟稳定可靠。
Matlab的第三方工具箱全套整合(强烈推荐)
Complex- for estimating temporal and spatial signal complexities
Computational Statistics
Coral- seismic waveform analysis
2007-8-2915:04
#1
littleboy
助理工程师
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JMatLink- Matlab Java classes
Kalman- Bayesian Kalman filter
Kalman Filter- filtering, smoothing and parameter estimation (using EM) for linear dynamical systems
DMsuite- differentiation matrix suite
DMTTEQ- design and test time domain equalizer design methods
DrawFilt- drawing digitaland analog filters
DSFWAV- spline interpolation with Dean wave solutions
FSBOX- stepwise forward and backward selection of features using linear regression
GABLE- geometric algebra tutorial
GAOT- genetic algorithm optimization
一种Farrow结构数字延时滤波器的设计
和数字滤波器。 文献[2] 提到的传统模拟延时器, 其作用原理是利用不同长度的传输线和切换开关实 现延时功能,但无法保证良好的延时精度。 而数字 延滤波器可以实现高精度延时,其设计方法主要 有时域、频域、混合域设计等。 文献[3] 和文献[4] 分别介绍了数字延时滤波器的时域和频域设计方 法,但针对不 同 的 延 时 值, 必 须 重 新 设 计 滤 波 器 系 数。 在实际环境中,对滤波器的要求是延时值可变, 所以,虽然时域或者频域延时滤波器设计实现简单, 却无法应对延时值实时可变的要求。 文献[5] 提出 Farrow 结构的数字延时滤波器,该延时滤波器无需 更新滤波器系数就可以完成对信号延时的实时调 整,克服了上述时域和频域设计方法的缺点。 文献 [6] 介绍了 Farrow 滤波器系数的求解方法,但都需 要满足一定条件,较为受限。
WANG Wei
( Southwest China Institute of Electronic Technology,Chengdu 610036,China)
Abstract:Although traditional digital delay filters have simple structures,the calculation of coefficients is complicated and their update speed can not satisfy constantly changing requirement when delay value chan鄄 ges,which results in limited engineering application. The digital delay filter with Farrow structure can be used for fractional delay filtering flexibly and efficiently without recalculation for filter coefficients when de鄄 lay value changes,and is easier to be implemented on Field Programmable Gate Array( FPGA) . This paper introduces a Farrow structure digital delay filter and proposes a method for calculating filter coefficients based on symmetric structure. Furthermore,weighted optimization strategy is used to obtain the final solu鄄 tions for filter coefficients. In the process of coefficient calculation,by analyzing the delay accuracy and er鄄 ror of designed Farrow filter,the weighting factor and filter order can be adjusted to improve delay accura鄄 cy. Finally,validity and practicability of the new method for the Farrow filter coefficients design is proved by computer simulation. Key words:digital time delay filter;fractional delay;Farrow structure;correction accuracy
Matlab的第三方工具箱大全(强烈推荐)
Matlab Toolboxes- acoustic doppler current profiler data processing- designing analog and digital filters- automatic integration of reusable embedded software- air-sea flux estimates in oceanography- developing scientific animations- estimation of parameters and eigenmodes of multivariateautoregressive methods- power spectrum estimation- computer vision tracking- auditory models- interval arithmetic- inference and learning for directed graphical models- calculating binaural cross-correlograms of sound- design of control systems with maximized feedback- for resampling, hypothesis testing and confidence intervalestimation- MEG and EEG data visualization and processing- equation viewer- interactive program for teaching the finite element method- for calibrating CCD cameras- non-stationary time series analysis and forecasting- for coupled hidden Markov modeling using maximumlikelihood EM- supervised and unsupervised classification algorithms- for analysis of Gaussian mixture models for data set clustering - cluster analysis- cluster analysis- speech analysis- solving problems in economics and finance- for estimating temporal and spatial signal complexities- seismic waveform analysis- kriging approximations to computer models- data assimilation in hydrological and hydrodynamic models- radar array processing- bifurcation analysis of delay differential equations- for removing noise from signals- solving differential equations on manifolds-- scientific image processing- Laplace transform inversion via the direct integration method - analysis and design of computer controlled systems with process-oriented models- differentiation matrix suite- design and test time domain equalizer design methods- drawing digital and analog filters- spline interpolation with Dean wave solutions- discrete wavelet transforms- graphical tool for nonsymmetric eigenproblems- separating light scattering and absorbance by extended multiplicative signal correction- fixed-point algorithm for ICA and projection pursuit- flight dynamics and control- fractional delay filter design- for independent components analysis- fuzzy model-based predictive control- Fourier-wavelet regularized deconvolution- fractal analysis for signal processing- stepwise forward and backward selection of features using linear regression- geometric algebra tutorial- genetic algorithm optimization- estimating and diagnosing heteroskedasticity in time series models- managing, analyzing and displaying data and metadata stored using the GCE data structure specification- growing cell structure visualization- fitting multilinear ANOVA models- geodetic calculations- growing hierarchical self-organizing map- general linear models- wrapper for GPIB library from National Instrument- generative topographic mapping, a model for densitymodeling and data visualization- gradient vector flow for finding 3-D object boundaries- converts HF radar data from radial current vectors to totalvectors- importing, processing and manipulating HF radar data- Hilbert transform by the rational eigenfunction expansionmethod- hidden Markov models- for hidden Markov modeling using maximum likelihood EM- auditory modeling- signal and image processing using ICA and higher orderstatistics- analysis of incomplete datasets- perception based musical analysis2007-8-29 15:04助理工程师- Matlab Java classes- Bayesian Kalman filter- filtering, smoothing and parameter estimation (using EM) for linear精华0 积分49 帖子76 水位164 技术分0 dynamical systems- state estimation of nonlinear systems- Kautz filter design- estimation of scaling exponents- low density parity check codes- wavelet lifting scheme on quincunx grids- Laguerre kernel estimation tool- Levenberg Marquardt with Adaptive Momentum algorithm for training feedforward neural networks- for exponential fitting, phase correction of quadrature data and slicing - Newton method for LP support vector machine for machine learning problems- robust control system design using the loop shaping design procedure- Lagrangian support vector machine for machine learning problems- functional neuroimaging- for multivariate autogressive modeling and cross-spectral estimation - analysis of microarray data- constructing test matrices, computing matrix factorizations, visualizing matrices, and direct search optimization- Monte Carlo analysis- Markov decision processes- graph and mesh partioning methods- maximum likelihood fitting using ordinary least squares algorithms- multidimensional code synthesis- functions for handling missing data values- geographic mapping tools- multi-objective control system design- multi-objective evolutionary algorithms- estimation of multiscaling exponents- analysis and regression on several data blocks simultaneously- feature extraction from raw audio signals for content-based music retrieval - multifractal wavelet model- neural network algorithms- data acquisition using the NiDAQ library- nonlinear economic dynamic models- numerical methods in Matlab text- design and simulation of control systems based on neural networks- neural net based identification of nonlinear dynamic systems- newton support vector machine for solving machine learning problems- non-uniform rational B-splines- analysis of multiway data with multilinear models- finite element development- pulse coupled neural networks- signal processing and analysis- probabilistic hierarchical interactive visualization, . functions for visual analysis of multivariate continuous data- simulation of n-DOF planar manipulators- pattern recognition- testing hyptheses about psychometric functions- proximal support vector machine for solving machine learning problems - vision research- multi-scale image processing- radial basis function neural networks- simulation of synchronous and asynchronous random boolean networks - sigma-point Kalman filters- basic multivariate data analysis and regression- robotics functions, . kinematics, dynamics and trajectory generation- robust calibration in stats- rainfall-runoff modelling- structure and motion- computation of conformal maps to polygonally bounded regions- smoothed data histogram- orthogonal grid maker- oceanographic analysis- sparse least squares- solver for local optimization problems- self-organizing map- solving sums of squares (SOS) optimization problems- statistical parametric mapping- smooth support vector machine for solving machine learning problems- for linear regression, feature selection, generation of data, and significance testing- statistical routines- pattern recognition methods- statistics- implements support vector machines- wavelet-based template learning and pattern classification- model-based document clustering- analyzing and synthesizing visual textures- continous 3-D minimum time orbit transfer around Earth- analyzing non-stationary signals using time-frequency distributions- tasks in tree-ring analysis- uni- and multivariate, stationary and non-stationary time series analysis- nonlinear time series analysis- harmonic analysis of tides- computing and modifying rank-revealing URV and UTV decompositions- wavelet analysis- orthogonal rotation of EOFs- variation Bayesian hidden Markov models- variational Bayesian mixtures of factor analyzers- VRML Molecule Toolbox, for animating results from molecular dynamicsexperiments- generates interactive VRML graphs and animations- computing and modifying symmetric rank-revealing decompositions - wave analysis for fatique and oceanography- frequency-warped signal processing- wavelet analysis- wavelet analysis- Laplace transform inversion via the Weeks method- NetCDF interface- wavelet-domain hidden Markov tree models- Wavelet-based inverse halftoning via deconvolution- weighted sequences clustering toolkit- XML parser- analyze single particle mass spectrum data- quantitative seismicity analysis。
ATF-54143资料翻译
安捷伦ATF-54143增强型高电子迁移率塑料封装低噪声放大噪数据手册描述安捷伦科技的ATF-54143具有高的动态范围、低噪声、增强型高电子迁移率，安置于表贴塑料封装SC-70（SOT-343）。
ATF-54143具有高增益、高线性和低噪声，使它成为理想的蜂窝状/PCS电台、多信道多点分配系统，和其它一些频率在450M到6G范围的系统。
表贴封装SOT-343引脚图和封装标志注：上图中提供情况和识别.“4F”=器件编码“X”=数据编码字符鉴别制造的年月特征：1、高线性度性2、增强型技术3、800微米门限宽4、低成本、小塑料封装SOT-343规格说明书2GHz；3V；60mA(Typ)1、36.2dBM三阶交调输出2、1dB压缩增益为20.4dBM3、0.5dB噪声系数4、相关增益为16.6dB应用1、蜂蜜状/PCS电台低噪声放大器。
2、WLAN、WLL/RLL低噪声放大器和多信道多点分配系统应用。
3、通用的离散增强型高电子迁移率对于其它极端低噪声的应用。
注：增强型技术需要正的偏置，因此排除需要负电压门限的传统耗尽型器件。
ATF-54143的绝对最大额定值产品的一致分布图注：1、操作这芯片的时候任何一个参数超过这最大值的时候就可能使芯片损坏。
2、假设直流静态条件。
3、当温度Tl>92度时，温度每上升一度降低6mW/c.4、热阻抗的测量通过150度的液体晶体的测量方法。
5、这器件可以处理10dBm 射频输入功率当IGS为2mA，Igs在P1db是驱动偏置电路所需要的，查看更多的应用信息。
6、分布数据样本大小为450的样本来自9个不同的晶圆，未来晶圆分配给这一产品可在任何地方上限和下限之间标称值。
7、测量了生产测试板，这电路代表基于生产设备的最佳噪声匹配，电路损耗嵌入式地从实际测量。
ATF-54143的电气说明书TA=25度时，射频参数测量在测试电路中的典型器件注：1、图5为测量使用的生产测试。
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1 Àkn ; 0rnrN À 1 X ðkÞWN N k¼0
ð3Þ
à Corresponding author.
E-mail addresses: tcc@.tw (C.-C. Tseng), lilee@.tw (S.-L. Lee). 0165-1684/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sigpro.2009.10.016
1. Introduction In many signal processing applications, there is a need for a delay which is a fraction of the sampling period. These applications include beam steering of antenna arrays, time adjustment in digital receivers, modeling of music instruments, speech coding and synthesis, comb filter design and analog digital conversion, etc. [1–6]. An excellent survey of fractional delay filter design is presented in tutorial paper [1]. Recently, the relationships among fractional delay, differentiator, Nyquist filter, lowpass filter and diamond-shaped filter have been established such that fractional delay becomes a versatile building block in the design of these practical filters [7–9]. The ideal frequency response of a fractional delay filter is given by DðoÞ ¼ e
abstract
In this paper, the design of fractional delay FIR filter is investigated. First, the interpolation formula of a discrete-time sequence is derived by using discrete Fourier transform (DFT). Then, the DFT-based interpolation formula is applied to design fractional delay FIR filter by using suitable index mapping. The filter coefficients are easily computed because a closed-form design is obtained. Next, design examples are demonstrated to show that the proposed DFT method has a smaller design error than those of the conventional Lagrange and window fractional delay FIR filters when using the same design parameters. Finally, the designed DFT-based fractional delay FIR filter is applied to design a digital differentiator and half-band filter. & 2009 Elsevier B.V. All rights reserved.
ÀjoðIþdÞ
where I is a positive integer and d is a fractional number in the interval [0,1). The transfer function of the FIR filter of length N used to approximate this specification is given by HðzÞ ¼
N À1 X r ¼0
hðr ÞzÀr
ð2Þ
So far, several methods of designing an FIR filter H(z) to fit fractional delay specification DðoÞ as closely as possible have been developed. Two typical approaches are Lagrange interpolation method and window method [1]. On the other hand, the discrete Fourier transform (DFT) is defined as follows: X ðkÞ ¼
0
in the time domain, so we should be able to use zero padding in the high frequency range of the DFT domain as a means of interpolating finite-duration, discrete-time signals. The details can be found in the literature [11–17]. So far, the DFT interpolation and fractional delay filter design are two independent research topics in signal processing area. The relation between them has not been investigated. The purpose of this paper is to study this relation such that DFT interpolation concept can be directly used to design fractional delay FIR filters. The main advantage is that the filter coefficients h(r) are easily computed because a closed-form design is obtained. This paper is organized as follows. In Section 2, the interpolation formulas for odd and even length N are derived. In Section 3, the interpolation formula is applied to design fractional delay FIR filter. There are two kinds of fractional delay filters to be designed. One concerns the case of even-length N, the other is the case of odd-length N. In Section 4, numerical examples are included in order to compare the filters designed using the proposed DFT method with conventional Lagrange and window fractional delay FIR filters. In Section 5, the designed DFTbased fractional delay FIR filter is also applied to design a digital differentiator and half-band filter. Finally, a conclusion is made. 2. DFT interpolation formula In this section, the DFT interpolation formula with even-length sequence is first derived. Then, the oddlength case is discussed. Given DFT X(k) of an even-length real-valued sequence x(n), let us define the zero-padded DFT as 8 N > > 0rkr À 1 > LX ðkÞ; > 2 > > > > 1 N N > > > LX ð Þ; k¼ > > 2 2 2 > > < N N þ 1rkrM À À 1 0 ; Xd ðkÞ ¼ ð4Þ 2 2 > > > > 1 N N > > > LX ð Þ; k¼MÀ > > 2 2 2 > > > > N > > þ 1rkrM À 1 LX ð k À M þ N Þ ; M À : 2 Also, we assume M is an integer multiple of N, say M=LN, where L is called interpolation factor. The above DFT has zero values in the high frequency range and satisfies the following conjugate symmetry condition: Xd ðM À kÞ ¼ Xd ðkÞÃ ; N 1rkr 2 ð5Þ