离散时间信号处理 英文版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

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1 Introduction1

2 Discrete-Time Signals and Systems9

2.0 Introduction9

2.1 Discrete-Time Signals10

2.2 Discrete-Time Systems17

2.2.1 Memoryless Systems18

2.2.2 Linear Systems19

2.2.3 Time-Invariant Systems20

2.2.4 Causality22

2.2.5 Stability22

2.3 LTI Systems23

2.4 Properties of Linear Time-Invariant Systems30

2.5 Linear Constant-Coefficient Difference Equations35

2.6 Frequency-Domain Representation of Discrete-Time Signals and Systems40

2.6.1 Eigenfunctions for Linear Time-Invariant Systems40

2.6.2 Suddenly Applied Complex Exponential Inputs46

2.7 Representation of Sequences by Fourier Transforms48

2.8 Symmetry Properties of the Fourier Transform54

2.9 Fourier Transform Theorems58

2.9.1 Linearity of the Fourier Transform59

2.9.2 Time Shifting and Frequency Shifting Theorem59

2.9.3 Time Reversal Theorem59

2.9.4 Differentiation in Frequency Theorem59

2.9.5 Parseval's Theorem60

2.9.6 The Convolution Theorem60

2.9.7 The Modulation or Windowing Theorem61

2.10 Discrete-Time Random Signals64

2.11 Summary70

Problems70

3 The z-Transform99

3.0 Introduction99

3.1 z-Transform99

3.2 Properties of the ROC for the z-Transform110

3.3 The Inverse z-Transform115

3.3.1 Inspection Method116

3.3.2 Partial Fraction Expansion116

3.3.3 Power Series Expansion122

3.4 z-Transform Properties124

3.4.1 Linearity124

3.4.2 Time Shifting125

3.4.3 Multiplication by an Exponential Sequence126

3.4.4 Differentiation of X（z）127

3.4.5 Conjugation of a Complex Sequence129

3.4.6 Time Reversal129

3.4.7 Convolution of Sequences130

3.4.8 Summary of Some z-Transform Properties131

3.5 z-Transforms and LTI Systems131

3.6 The Unilateral z-Transform135

3.7 Summary137

Problems138

4 Sampling of Continuous-Time Signals153

4.0 Introduction153

4.1 Periodic Sampling153

4.2 Frequency-Domain Representation of Sampling156

4.3 Reconstruction of a Bandlimited Signal from Its Samples163

4.4 Discrete-Time Processing of Continuous-Time Signals167

4.4.1 Discrete-Time LTI Processing of Continuous-Time Signals168

4.4.2 Impulse Invariance173

4.5 Continuous-Time Processing of Discrete-Time Signals175

4.6 Changing the Sampling Rate Using Discrete-Time Processing179

4.6.1 Sampling Rate Reduction by an Integer Factor180

4.6.2 Increasing the Sampling Rate by an Integer Factor184

4.6.3 Simple and Practical Interpolation Filters187

4.6.4 Changing the Sampling Rate by a Noninteger Factor190

4.7 Multirate Signal Processing194

4.7.1 Interchange of Filtering with Compressor/Expander194

4.7.2 Multistage Decimation and Interpolation195

4.7.3 Polyphase Decompositions197

4.7.4 Polyphase Implementation of Decimation Filters199

4.7.5 Polyphase Implementation of Interpolation Filters200

4.7.6 Multirate Filter Banks201

4.8 Digital Processing of Analog Signals205

4.8.1 Prefiltering to Avoid Aliasing206

4.8.2 A/D Conversion209

4.8.3 Analysis of Quantization Errors214

4.8.4 D/A Conversion221

4.9 Oversampling and Noise Shaping in A/D and D/A Conversion224

4.9.1 Oversampled A/D Conversion with Direct Quantization225

4.9.2 Oversampled A/D Conversion with Noise Shaping229

4.9.3 Oversampling and Noise Shaping in D/A Conversion234

4.10 Summary236

Problems237

5 Transform Analysis of Linear Time-Invariant Systems274

5.0 Introduction274

5.1 The Frequency Response of LTI Systems275

5.1.1 Frequency Response Phase and Group Delay275

5.1.2 Illustration of Effects of Group Delay and Attenuation278

5.2 System Functions—Linear Constant-Coefficient Difference Equations283

5.2.1 Stability and Causality285

5.2.2 Inverse Systems286

5.2.3 Impulse Response for Rational System Functions288

5.3 Frequency Response for Rational System Functions290

5.3.1 Frequency Responseof 1st-Order Systems292

5.3.2 Examples with Multiple Poles and Zeros296

5.4 Relationship between Magnitude and Phase301

5.5 All-Pass Systems305

5.6 Minimum-Phase Systems311

5.6.1 Minimum-Phase and All-Pass Decomposition311

5.6.2 Frequency-Response Compensation of Non-Minimum-Phase Systems313

5.6.3 Properties of Minimum-Phase Systems318

5.7 Linear Systems with Generalized Linear Phase322

5.7.1 Systems with Linear Phase322

5.7.2 Generalized Linear Phase326

5.7.3 Causal Generalized Linear-Phase Systems328

5.7.4 Relation of FIR Linear-Phase Systems to Minimum-Phase Systems338

5.8 Summary340

Prohlems341

6 Structures for Discrete-Time Systems374

6.0 Introduction374

6.1 Block Diagram Representation of Linear Constant-Coefficient Difference Equations375

6.2 Signal Flow Graph Representation382

6.3 Basic Structures for IIR Systems388

6.3.1 Direct Forms388

6.3.2 Cascade Form390

6.3.3 Parallel Form393

6.3.4 Feedback in IIR Systems395

6.4 Transposed Forms397

6.5 Basic Network Structures for FIR Systems401

6.5.1 Direct Form401

6.5.2 Cascade Form402

6.5.3 Structures for Linear-Phase FIR Systems403

6.6 Lattice Filters405

6.6.1 FIR Lattice Filters406

6.6.2 A11-Pole Lattice Structure412

6.6.3 Generalization of Lattice Systems415

6.7 Overview of Finite-Precision Numerical Effects415

6.7.1 Number Representations415

6.7.2 Quantization in Implementing Systems419

6.8 The Effects of Coefficient Quantization421

6.8.1 Effects of Coefficient Quantization in IIR Systems422

6.8.2 Example of Coefficient Quantization in an Elliptic Filter423

6.8.3 P0lesof Quantized 2nd-Order Sections427

6.8.4 Effects of Coefficient Quantization in FIR Systems429

6.8.5 Example of Quantization of an Optimum FIR Filter431

6.8.6 Maintaining Linear Phase434

6.9 Effects of Round-off Noise in Digital Filters436

6.9.1 Analysis of the Direct Form IIR Structures436

6.9.2 Scaling in Fixed-Point Implementations of IIR Systems445

6.9.3 Example of Analysis of a Cascade IIR Structure448

6.9.4 Analysis of Direct-Form FIR Systems453

6.9.5 Floating-Point Realizations of Discrete-Time Systems458

6.10 Zero-Input Limit Cycles in Fixed-Point Realizations of IIR Digital Filters459

6.10.1 Limit Cycles Owing to Round-off and Truncation459

6.10.2 Limit Cycles Owing to Overflow462

6.10.3 Avoiding Limit Cycles463

6.11 Summary463

Problems464

7 Filter Design Techniques493

7.0 Introduction493

7.1 Filter Specifications494

7.2 Design of Discrete-Time IIR Filters from Continuous-Time Filters496

7.2.1 Filter Design by Impulse Invariance497

7.2.2 Bilinear Transformation504

7.3 Discrete-Time Butterworth,Chebyshev and Elliptic Filters508

7.3.1 Examples of IIR Filter Design509

7.4 Frequency Transformations of Lowpass IIR Filters526

7.5 Design ofFIR Filters by Windowing533

7.5.1 Properties of Commonly Used Windows535

7.5.2 Incorporation of Generalized Linear Phase538

7.5.3 The Kaiser Window Filter Design Method541

7.6 Examples of FIR Filter Design by the Kaiser Window Method545

7.6.1 Lowpass Filter545

7.6.2 Highpass Filter547

7.6.3 Discrete-Time Differentiators550

7.7 Optimum Approximations ofFIR Filters554

7.7.1 Optimal Type Ⅰ Lowpass Filters559

7.7.2 Optimal Type Ⅱ Lowpass Filters565

7.7.3 The Parks-McClellan Algorithm566

7.7.4 Characteristics of Optimum FIR Filters568

7.8 Examples of FIR Equiripple Approximation570

7.8.1 Lowpass Filter570

7.8.2 Compensation for Zero-Order Hold571

7.8.3 Bandpass Filter576

7.9 Comments on IIR and FIR Discrete-Time Filters578

7.10 Design of an Upsampling Filter579

7.11 Summary582

Problems582

8 The Discrete Fourier Transform623

8.0 Introduction623

8.1 Representation of Periodic Sequences:The Discrete Fourier Series624

8.2 Properties ofthe DFS628

8.2.1 Linearity629

8.2.2 Shift of a Sequence629

8.2.3 Duality629

8.2.4 Symmetry Properties630

8.2.5 Periodic Convolution630

8.2.6 Summary of Properties of the DFS Representation of Periodic Sequences633

8.3 The Fourier Transform of Periodic Signals633

8.4 Sampling the Fourier Transform638

8.5 Fourier Representation of Finite-Duration Sequences642

8.6 Properties ofthe DFT647

8.6.1 Linearity647

8.6.2 Circular Shift of a Sequence648

8.6.3 Duality650

8.6.4 Symmetry Properties653

8.6.5 Circular Convolution654

8.6.6 Summary of Properties of the DFT659

8.7 Linear Convolution Using the DFT660

8.7.1 Linear Convolution of Two Finite-Length Sequences661

8.7.2 Circular Convolution as Linear Convolution with Aliasing661

8.7.3 Implementing Linear Time-Invariant Systems Using the DFT667

8.8 The Discrete Cosine Transform（DCT）673

8.8.1 Definitions ofthe DCT673

8.8.2 Definition of the DCT-1 and DCT-2675

8.8.3 Relationship between the DFT and the DCT-1676

8.8.4 Relationship between the DFT and the DCT-2678

8.8.5 Energy Compaction Property of the DCT-2679

8.8.6 Applications of the DCT682

8.9 Summary683

Problems684

9 Computation of the Discrete Fourier Transform716

9.0 Introduction716

9.1 Direct Computation of the Discrete Fourier Transform718

9.1.1 Direct Evaluation of the Definition of the DFT718

9.1.2 The Goertzel Algorithm719

9.1.3 Exploiting both Symmetry and Periodicity722

9.2 Decimation-in-Time FFr Algorithms723

9.2.1 Generalization and Programming the FFT731

9.2.2 In-Place Computations731

9.2.3 Alternative Forms734

9.3 Decimation-in-Frequency FFT Algorithms737

9.3.1 In-Place Computation741

9.3.2 Alternative Forms741

9.4 Practical Considerations743

9.4.1 Indexing743

9.4.2 Coefficients745

9.5 More General FFT Algorithms745

9.5.1 Algorithms for Composite Values of N746

9.5.2 Optimized FFr Algorithms748

9.6 Implementation of the DFT Using Convolution748

9.6.1 Overview of the Winograd Fourier Transform Algorithm749

9.6.2 The Chirp Transform Algorithm749

9.7 Effects of Finite Register Length754

9.8 Summary762

Problems763

10 Fourier Analysis of Signals Using the Discrete Fourier Transform792

10.0 Introduction792

10.1 Fourier Analysis of Signals Using the DFT793

10.2 DFT Analysis of Sinusoidal Signals797

10.2.1 The Effect of Windowing797

10.2.2 Properties of the Windows800

10.2.3 The Effect of Spectral Sampling801

10.3 The Time-Dependent Fourier Transform811

10.3.1 Invertibility ofX[n,）815

10.3.2 Filter Bank Interpretation of X[n,）816

10.3.3 The Effect of the Window817

10.3.4 Sampling in Time and Frequency819

10.3.5 The Overlap－Add Method of Reconstruction822

10.3.6 Signal Processing Based on the Time-Dependent Fourier Transform825

10.3.7 Filter Bank Interpretation of the Time-Dependent Fourier Transform826

10.4 Examples of Fourier Analysis of Nonstationary Signals829

10.4.1 Time-Dependent Fourier Analysis of Speech Signals830

10.4.2 Time-Dependent Fourier Analysis of Radar Signals834

10.5 Fourier Analysis of Stationary Random Signals:the Periodogram836

10.5.1 The Periodogram837

10.5.2 Properties of the Periodogram839

10.5.3 Periodogram Averaging843

10.5.4 Computation of Average Periodograms Using the DFT845

10.5.5 An Example of Periodogram Analysis845

10.6 Spectrum Analysis of Random Signals849

10.6.1 Computing Correlation and Power Spectrum Estimates Using the DFT853

10.6.2 Estimating the Power Spectrum of Quantization Noise855

10.6.3 Estimating the Powet Spectrum of Speech860

10.7 Summary862

Problems864

11 Parametric Signal Modeling890

11.0 Introduction890

11.1 All-Pole Modeling of Signals891

11.1.1 Least-Squares Approximation892

11.1.2 Least-Squares Inverse Model892

11.1.3 Linear Prediction Formulation of All-Pole Modeling895

11.2 Deterministic and Random Signal Models896

11.2.1 All-Pole Modeling of Finite-Energy Deterministic Signals896

11.2.2 Modeling of Random Signals897

11.23 Minimum Mean-Squared Error898

11.2.4 Autocorrelation Matching Property898

11.2.5 Determination of the Gain Parameter G899

11.3 Estimation of the Correlation Functions900

11.3.1 The Autocorrelation Method900

11.3.2 The Covariance Method903

11.3.3 Comparison of Methods904

11.4 Model Order905

11.5 All-Pole Spectrum Analysis907

11.5.1 All-Pole Analysis of Speech Signals908

11.5.2 Pole Locations911

11.5.3 All-Pole Modeling of Sinusoidal Signals913

11.6 Solution of the Autocorrelation Normal Equations915

11.6.1 The Levinson－Durbin Recursion916

11.6.2 Derivation of the Levinson－Durbin Algorithm917

11.7 Lattice Filters920

11.7.1 Prediction Error Lattice Network921

11.7.2 All-Pole Model Lattice Network923

11.7.3 Direct Computation of the k-Parameters925

11.8 Summary926

Problems927

12 Discrete Hilbert Transforms942

12.0 Introduction942

12.1 Real-and Imaginary-Part Sufficiency of the Fourier Transform944

12.2 Sufficiency Theorems for Finite-Length Sequences949

12.3 Relationships Between Magnitude and Phase955

12.4 Hilbert Transform Relations for Complex Sequences956

12.4.1 Design of Hilbert Transformers960

12.4.2 Representation of Bandpass Signals963

12.4.3 Bandpass Sampling966

12.5 Summary969

Problems969

13 Cepstrum Analysis and Homomorphic Deconvolution980

13.0 Introduction980

13.1 Definition of the Cepstrum981

13.2 Definition of the Complex Cepstrum982

13.3 Properties of the Complex Logarithm984

13.4 Alternative Expressions for the Complex Cepstrum985

13.5 Properties of the Complex Cepstrum986

13.5.1 Exponential Sequences986

13.5.2 Minimum-Phase and Maximum-Phase Sequences989

13.5.3 Relationship Between the Real Cepstrum and the Complex Cepstrum990

13.6 Computation ofthe Complex Cepstrum992

13.6.1 Phase Unwrapping993

13.6.2 Computation of the Complex Cepstrum Using the Logarithmic Derivative996

13.6.3 Minimum-Phase Realizations for Minimum-Phase Sequences998

13.6.4 Recursive Computation of the Complex Cepstrum for Minimum-and Maximum-Phase Sequences998

13.6.5 The Use of Exponential Weighting1000

13.7 Computation of the Complex Cepstrum Using Polynomial Roots1001

13.8 Deconvolution Using the Complex Cepstrum1002

13.8.1 Minimum-Phase/Allpass Homomorphic Deconvolution1003

13.8.2 Minimum-Phase/Maximum-Phase Homomorphic Deconvolution1004

13.9 The Complex Cepstrum for a Simple Multipath Model1006

13.9.1 Computation of the Complex Cepstrum bv z-Transform Analysis1009

13.9.2 Computation of the Cepstrum Using the DFT1013

13.9.3 Homomorphic Deconvolution for the Multipath Model1016

13.9.4 Minimum-Phase Decomposition1017

13.9.5 Generalizations1024

13.10 Applications to Speech Processing1024

13.10.1 The Speech Model1024

13.10.2 Example of Homomorphic Deconvolution of Speech1028

13.10.3 Estimating the Parameters of the Speech Model1030

13.10.4 Applications1032

13.11 Summary1032

Problems1034

A Random Signals1043

B Continuous-Time Filters1056

C Answers to Selected Basic Problems1061

Bibliography1082

Index1091