本书包含了数字信号处理（DSP）系统分析和设计的所有重要内容，采用现代的方法讨论问题，包括MATLAB范例和其他仿真工具的介绍。主要内容包括：数字信号处理系统的使用，如何用多项式和比值多项式逼近转移函数并保持转移函数的特性，为什么在应用中要将转移函数用适当的结构进行图形表示，滤波器组和小波设计，以及信号时域和频域表述的相互关系。

经典原版书库

本书将理论与实际有机融合，涵盖了数字信号处理（DSP）分析和设计的所有重要内容，提供了数字信号处理这一前沿技术领域难得的设计理念和方法。本书不仅可作为高等院校电子、通信等专业本科生或研究生教材，还可作为工程技术人员DSP设计方面的参考用书。
第2版在上一版的基础上，扩充了滤波器组和小波分析的内容，新增了随机信号处理、谱估计和求解差分方程的内容，数学推导中给出了易于读者理解的步骤。第2版还提供了120个范例、20个案例研究、约400道练习题。此外，第2版还有一大新特点——每章末增加了一节“Do-it-Yourself”，使读者通过MATLAB实验获得解决实际信号处理问题的亲身体验。

（巴西）Paulo S. R. Diniz; Eduardo A. B. da Silva; Sergio L. Netto 著 里约热内卢联邦大学：Paulo S. R. Diniz Poli 巴西里约热内卢联邦大学（UFRJ）电子与计算机工程系和COPPE/UFRJ研究生院教授，他还是IEEE会士。 Eduardo A. B. da Silva Poli 巴西里约热内卢联邦大学（UFRJ）电子与计算机工程系和COPPE/UFRJ研究生院副教授。 Sergio L. Netto Poli 巴西里约热内卢联邦大学（UFRJ）电子与计算机工程系和COPPE/UFRJ研究生院副教授。

Preface page　xvi
Introduction 1
1 Discrete-time signals and systems 5
1.1 Introduction 5
1.2 Discrete-time signals 6
1.3 Discrete-time systems 10
1.3.1 Linearity 10
1.3.2 Time invariance 11
1.3.3 Causality 11
1.3.4 Impulse response and convolution sums 14
1.3.5 Stability 16
1.4 Difference equations and time-domain response 17
1.4.1 Recursive × nonrecursive systems 21
1.5 Solving difference equations 22
1.5.1 Computing impulse responses 31
1.6 Sampling of continuous-time signals 33
1.6.1 Basic principles 34
1.6.2 Sampling theorem 34
1.7 Random signals 53
1.7.1 Random variable 54
1.7.2 Random processes 58
1.7.3 Filtering a random signal 60
1.8 Do-it-yourself: discrete-time signals and systems 62
1.9 Discrete-time signals and systems with Matlab 67
1.10 Summary 68
1.11 Exercises 68
2 The z and Fourier transforms 75
2.1 Introduction 75
2.2 Definition of the z transform 76
2.3 Inverse z transform 83
2.3.1 Computation based on residue theorem 84
2.3.2 Computation based on partial-fraction expansions 87
2.3.3 Computation based on polynomial division 90
2.3.4 Computation based on series expansion 92
2.4 Properties of the z transform 94
2.4.1 Linearity 94
2.4.2 Time reversal 94
2.4.3 Time-shift theorem 95
2.4.4 Multiplication by an exponential 95
2.4.5 Complex differentiation 95
2.4.6 Complex conjugation 96
2.4.7 Real and imaginary sequences 97
2.4.8 Initial-value theorem 97
2.4.9 Convolution theorem 98
2.4.10 Product of two sequences 98
2.4.11 Parseval’s theorem 100
2.4.12 Table of basic z transforms 101
2.5 Transfer functions 104
2.6 Stability in the z domain 106
2.7 Frequency response 109
2.8 Fourier transform 115
2.9 Properties of the Fourier transform 120
2.9.1 Linearity 120
2.9.2 Time reversal 120
2.9.3 Time-shift theorem 120
2.9.4 Multiplication by a complex exponential (frequency shift, modulation) 120
2.9.5 Complex differentiation 120
2.9.6 Complex conjugation 121
2.9.7 Real and imaginary sequences 121
2.9.8 Symmetric and antisymmetric sequences 122
2.9.9 Convolution theorem 123
2.9.10 Product of two sequences 123
2.9.11 Parseval’s theorem 123
2.10 Fourier transform for periodic sequences 123
2.11 Random signals in the transform domain 125
2.11.1 Power spectral density 125
2.11.2 White noise 128
2.12 Do-it-yourself: the z and Fourier transforms 129
2.13 The z and Fourier transforms with Matlab 135
2.14 Summary 137
2.15 Exercises 137
3 Discrete transforms 143
3.1 Introduction 143
3.2 Discrete Fourier transform 144
3.3 Properties of the DFT 153
3.3.1 Linearity 153
3.3.2 Time reversal 153
3.3.3 Time-shift theorem 153
3.3.4 Circular frequency-shift theorem (modulation theorem) 156
3.3.5 Circular convolution in time 157
3.3.6 Correlation 158
3.3.7 Complex conjugation 159
3.3.8 Real and imaginary sequences 159
3.3.9 Symmetric and antisymmetric sequences 160
3.3.10 Parseval’s theorem 162
3.3.11 Relationship between the DFT and the z transform 163
3.4 Digital filtering using the DFT 164
3.4.1 Linear and circular convolutions 164
3.4.2 Overlap-and-add method 168
3.4.3 Overlap-and-save method 171
3.5 Fast Fourier transform 175
3.5.1 Radix-2 algorithm with decimation in time 176
3.5.2 Decimation in frequency 184
3.5.3 Radix-4 algorithm 187
3.5.4 Algorithms for arbitrary values of N 192
3.5.5 Alternative techniques for determining the DFT 193
3.6 Other discrete transforms 194
3.6.1 Discrete transforms and Parseval’s theorem 195
3.6.2 Discrete transforms and orthogonality 196
3.6.3 Discrete cosine transform 199
3.6.4 A family of sine and cosine transforms 203
3.6.5 Discrete Hartley transform 205
3.6.6 Hadamard transform 206
3.6.7 Other important transforms 207
3.7 Signal representations 208
3.7.1 Laplace transform 208
3.7.2 The z transform 208
3.7.3 Fourier transform (continuous time) 209
3.7.4 Fourier transform (discrete time) 209
3.7.5 Fourier series 210
3.7.6 Discrete Fourier transform 210
3.8 Do-it-yourself: discrete transforms 211
3.9 Discrete transforms with Matlab 215
3.10 Summary 216
3.11 Exercises 217
4 Digital filters 222
4.1 Introduction 222
4.2 Basic structures of nonrecursive digital filters 222
4.2.1 Direct form 223
4.2.2 Cascade form 224
4.2.3 Linear-phase forms 225
4.3 Basic structures of recursive digital filters 232
4.3.1 Direct forms 232
4.3.2 Cascade form 236
4.3.3 Parallel form 237
4.4 Digital network analysis 241
4.5 State-space description 244
4.6 Basic properties of digital networks 246
4.6.1 Tellegen’s theorem 246
4.6.2 Reciprocity 248
4.6.3 Interreciprocity 249
4.6.4 Transposition 249
4.6.5 Sensitivity 250
4.7 Useful building blocks 257
4.7.1 Second-order building blocks 257
4.7.2 Digital oscillators 260
4.7.3 Comb filter 261
4.8 Do-it-yourself: digital filters 263
4.9 Digital filter forms with Matlab 266
4.10 Summary 270
4.11 Exercises 270
5 FIR filter approximations 277
5.1 Introduction 277
5.2 Ideal characteristics of standard filters 277
5.2.1 Lowpass, highpass, bandpass, and bandstop filters 278
5.2.2 Differentiators 280
5.2.3 Hilbert transformers 281
5.2.4 Summary 283
5.3 FIR filter approximation by frequency sampling 283
5.4 FIR filter approximation with window functions 291
5.4.1 Rectangular window 294
5.4.2 Triangular windows 295
5.4.3 Hamming and Hann windows 296
5.4.4 Blackman window 297
5.4.5 Kaiser window 299
5.4.6 Dolph–Chebyshev window 306
5.5 Maximally flat FIR filter approximation 309
5.6 FIR filter approximation by optimization 313
5.6.1 Weighted least-squares method 317
5.6.2 Chebyshev method 321
5.6.3 WLS--Chebyshev method 327
5.7 Do-it-yourself: FIR filter approximations 333
5.8 FIR filter approximation with Matlab 336
5.9 Summary 342
5.10 Exercises 343
6 IIR filter approximations 349
6.1 Introduction 349
6.2 Analog filter approximations 350
6.2.1 Analog filter specification 350
6.2.2 Butterworth approximation 351
6.2.3 Chebyshev approximation 353
6.2.4 Elliptic approximation 356
6.2.5 Frequency transformations 359
6.3 Continuous-time to discrete-time transformations 368
6.3.1 Impulse-invariance method 368
6.3.2 Bilinear transformation method 372
6.4 Frequency transformation in the discrete-time domain 378
6.4.1 Lowpass-to-lowpass transformation 379
6.4.2 Lowpass-to-highpass transformation 380
6.4.3 Lowpass-to-bandpass transformation 380
6.4.4 Lowpass-to-bandstop transformation 381
6.4.5 Variable-cutoff filter design 381
6.5 Magnitude and phase approximation 382
6.5.1 Basic principles 382
6.5.2 Multivariable function minimization method 387
6.5.3 Alternative methods 389
6.6 Time-domain approximation 391
6.6.1 Approximate approach 393
6.7 Do-it-yourself: IIR filter approximations 394
6.8 IIR filter approximation with Matlab 399
6.9 Summary 403
6.10 Exercises 404
7 Spectral estimation 409
7.1 Introduction 409
7.2 Estimation theory 410
7.3 Nonparametric spectral estimation 411
7.3.1 Periodogram 411
7.3.2 Periodogram variations 413
7.3.3 Minimum-variance spectral estimator 416
7.4 Modeling theory 419
7.4.1 Rational transfer-function models 419
7.4.2 Yule–Walker equations 423
7.5 Parametric spectral estimation 426
7.5.1 Linear prediction 426
7.5.2 Covariance method 430
7.5.3 Autocorrelation method 431
7.5.4 Levinson–Durbin algorithm 432
7.5.5 Burg’s method 434
7.5.6 Relationship of the Levinson–Durbin algorithm to
a lattice structure 438
7.6 Wiener filter 438
7.7 Other methods for spectral estimation 441
7.8 Do-it-yourself: spectral estimation 442
7.9 Spectral estimation with Matlab 449
7.10 Summary 450
7.11 Exercises 451
8 Multirate systems 455
8.1 Introduction 455
8.2 Basic principles 455
8.3 Decimation 456
8.4 Interpolation 462
8.4.1 Examples of interpolators 464
8.5 Rational sampling-rate changes 465
8.6 Inverse operations 466
8.7 Noble identities 467
8.8 Polyphase decompositions 469
8.9 Commutator models 471
8.10 Decimation and interpolation for efficient filter implementation 474
8.10.1 Narrowband FIR filters 474
8.10.2 Wideband FIR filters with narrow transition bands 477
8.11 Overlapped block filtering 479
8.11.1 Nonoverlapped case 480
8.11.2 Overlapped input and output 483
8.11.3 Fast convolution structure I 487
8.11.4 Fast convolution structure II 487
8.12 Random signals in multirate systems 490
8.12.1 Interpolated random signals 491
8.12.2 Decimated random signals 492
8.13 Do-it-yourself: multirate systems 493
8.14 Multirate systems with Matlab 495
8.15 Summary 497
8.16 Exercises 498
9 Filter banks 503
9.1 Introduction 503
9.2 Filter banks 503
9.2.1 Decimation of a bandpass signal 504
9.2.2 Inverse decimation of a bandpass signal 505
9.2.3 Critically decimated M -band filter banks 506
9.3 Perfect reconstruction 507
9.3.1 M -band filter banks in terms of polyphase components 507
9.3.2 Perfect reconstruction M -band filter banks 509
9.4 Analysis of M -band filter banks 517
9.4.1 Modulation matrix representation 518
9.4.2 Time-domain analysis 520
9.4.3 Orthogonality and biorthogonality in filter banks 529
9.4.4 Transmultiplexers 534
9.5 General two-band perfect reconstruction filter banks 535
9.6 QMF filter banks 540
9.7 CQF filter banks 543
9.8 Block transforms 548
9.9 Cosine-modulated filter banks 554
9.9.1 The optimization problem in the design of cosine-modulated filter banks 559
9.10 Lapped transforms 563
9.10.1 Fast algorithms and biorthogonal LOT 573
9.10.2 Generalized LOT 576
9.11 Do-it-yourself: filter banks 581
9.12 Filter banks with Matlab 594
9.13 Summary 594
9.14 Exercises 595
10　Wavelet transforms 599
10.1 Introduction 599
10.2 Wavelet transforms 599
10.2.1 Hierarchical filter banks 599
10.2.2 Wavelets 601
10.2.3 Scaling functions 605
10.3 Relation between x(t) and x(n) 606
10.4 Wavelet transforms and time–frequency analysis 607
10.4.1 The short-time Fourier transform 607
10.4.2 The continuous-time wavelet transform 612
10.4.3 Sampling the continuous-time wavelet transform:
the discrete wavelet transform 614
10.5 Multiresolution representation 617
10.5.1 Biorthogonal multiresolution representation 620
10.6 Wavelet transforms and filter banks 623
10.6.1 Relations between the filter coefficients 629
10.7 Regularity 633
10.7.1 Additional constraints imposed on the filter banks
due to the regularity condition 634
10.7.2 A practical estimate of regularity 635
10.7.3 Number of vanishing moments 636
10.8 Examples of wavelets 638
10.9 Wavelet transforms of images 641
10.10　Wavelet transforms of finite-length signals 646
10.10.1　Periodic signal extension 646
10.10.2　Symmetric signal extensions 648
10.11　 Do-it-yourself: wavelet transforms 653
10.12　Wavelets with Matlab 659
10.13　Summary 664
10.14　Exercises 665
11　Finite-precision digital signal processing 668
11.1 Introduction 668
11.2 Binary number representation 670
11.2.1 Fixed-point representations 670
11.2.2 Signed power-of-two representation 672
11.2.3 Floating-point representation 673
11.3 Basic elements 674
11.3.1 Properties of the two’s-complement representation 674
11.3.2 Serial adder 674
11.3.3 Serial multiplier 676
11.3.4 Parallel adder 684
11.3.5 Parallel multiplier 684
11.4 Distributed arithmetic implementation 685
11.5 Product quantization 691
11.6 Signal scaling 697
11.7 Coefficient quantization 706
11.7.1 Deterministic sensitivity criterion 708
11.7.2 Statistical forecast of the wordlength 711
11.8 Limit cycles 715
11.8.1 Granular limit cycles 715
11.8.2 Overflow limit cycles 717
11.8.3 Elimination of zero-input limit cycles 719
11.8.4 Elimination of constant-input limit cycles 725
11.8.5 Forced-response stability of digital filters with
nonlinearities due to overflow 729
11.9 Do-it-yourself: finite-precision digital signal processing 732
11.10　 Finite-precision digital signal processing with Matlab 735
11.11　 Summary 735
11.12　 Exercises 736
12　Efficient FIR structures 740
12.1 Introduction 740
12.2 Lattice form 740
12.2.1 Filter banks using the lattice form 742
12.3 Polyphase form 749
12.4 Frequency-domain form 750
12.5 Recursive running sum form 750
12.6 Modified-sinc filter 752
12.7 Realizations with reduced number of arithmetic operations 753
12.7.1 Prefilter approach 753
12.7.2 Interpolation approach 756
12.7.3 Frequency-response masking approach 760
12.7.4 Quadrature approach 771
12.8 Do-it-yourself: efficient FIR structures 776
12.9 Efficient FIR structures with Matlab 781
12.10　Summary 782
12.11　 Exercises 782
13　Efficient IIR structures 787
13.1 Introduction 787
13.2 IIR parallel and cascade filters 787
13.2.1 Parallel form 788
13.2.2 Cascade form 790
13.2.3 Error spectrum shaping 795
13.2.4 Closed-form scaling 797
13.3 State-space sections 800
13.3.1 Optimal state-space sections 801
13.3.2 State-space sections without limit cycles 806
13.4 Lattice filters 815
13.5 Doubly complementary filters 822
13.5.1 QMF filter bank implementation 826
13.6 Wave filters 828
13.6.1 Motivation 829
13.6.2 Wave elements 832
13.6.3 Lattice wave digital filters 848
13.7 Do-it-yourself: efficient IIR structures 855
13.8 Efficient IIR structures with Matlab 857
13.9 Summary 857
13.10　Exercises 858
References 863
Index 877