数字信号处理 第4版 英文版PDF|Epub|txt|kindle电子书版本网盘下载

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1 Introduction1

1.1 Signals, Systems, and Signal Processing2

1.1.1 Basic Elements of a Digital Signal Processing System4

1.1.2 Advantages of Digital over Analog Signal Processing5

1.2 Classification of Signals6

1.2.1 Multichannel and Multidimensional Signals6

1.2.2 Continuous-Time Versus Discrete-Time Signals9

1.2.3 Continuous-Valued Versus Discrete-Valued Signals10

1.2.4 Deterministic Versus Random Signals11

1.3 The Concept of Frequency in Continuous-Time and Discrete-Time Signals12

1.3.1 Continuous-Time Sinusoidal Signals12

1.3.2 Discrete-Time Sinusoidal Signals14

1.3.3 Harmonically Related Complex Exponentials17

1.4 Analog-to-Digital and Digital-to-Analog Conversion19

1.4.1 Sampling of Analog Signals21

1.4.2 The Sampling Theorem26

1.4.3 Quantization of Continuous-Amplitude Signals31

1.4.4 Quantization of Sinusoidal Signals34

1.4.5 Coding of Quantized Samples35

1.4.6 Digital-to-Analog Conversion36

1.4.7 Analysis of Digital Signals and Systems Versus Discrete-Time Signals and Systems36

1.5 Summary and References37

Problems37

2 Discrete-Time Signals and Systems41

2.1 Discrete-Time Signals42

2.1.1 Some Elementary Discrete-Time Signals43

2.1.2 Classification of Discrete-Time Signals45

2.1.3 Simple Manipulations of Discrete-Time Signals50

2.2 Discrete-Time Systems53

2.2.1 Input-Output Description of Systems54

2.2.2 Block Diagram Representation of Discrete-Time Systems57

2.2.3 Classification of Discrete-Time Systems59

2.2.4 Interconnection of Discrete-Time Systems67

2.3 Analysis of Discrete-Time Linear Time-Invariant Systems69

2.3.1 Techniques for the Analysis of Linear Systems69

2.3.2 Resolution of a Discrete-Time Signal into Impulses71

2.3.3 Response of LTI Systems to Arbitrary Inputs: The Convolution Sum73

2.3.4 Properties of Convolution and the Interconnection of LTI Systems80

2.3.5 Causal Linear Time-Invariant Systems83

2.3.6 Stability of Linear Time-Invariant Systems85

2.3.7 Systems with Finite-Duration and Infinite-Duration Impulse Response88

2.4 Discrete-Time Systems Described by Difference Equations89

2.4.1 Recursive and Nonrecursive Discrete-Time Systems90

2.4.2 Linear Time-Invariant Systems Characterized by Constant-Coefficient Difference Equations93

2.4.3 Solution of Linear Constant-Coefficient Difference Equations98

2.4.4 The Impulse Response of a Linear Time-Invariant Recursive System106

2.5 Implementation of Discrete-Time Systems109

2.5.1 Structures for the Realization of Linear Time-Invariant Systems109

2.5.2 Recursive and Nonrecursive Realizations of FIR Systems113

2.6 Correlation of Discrete-Time Signals116

2.6.1 Crosscorrelation and Autocorrelation Sequences118

2.6.2 Properties of the Autocorrelation and Crosscorrelation Sequences120

2.6.3 Correlation of Periodic Sequences123

2.6.4 Input-Output Correlation Sequences125

2.7 Summary and References128

Problems129

3 The Z-Transform and Its Application to the Analysis of LTI Systems147

3.1 The z-Transform147

3.1.1 The Direct z-Transform147

3.1.2 The Inverse z-Transform156

3.2 Properties of the z-Transform157

3.3 Rational z-Transforms170

3.3.1 Poles and Zeros170

3.3.2 Pole Location and Time-Domain Behavior for Causal Signals174

3.3.3 The System Function of a Linear Time-Invariant System177

3.4 Inversion of the z-Transform180

3.4.1 The Inverse z -Transform by Contour Integration180

3.4.2 The Inverse z-Transform by Power Series Expansion182

3.4.3 The Inverse z-Transform by Partial-Fraction Expansion184

3.4.4 Decomposition of Rational z-Transforms192

3.5 Analysis of Linear Time-Invariant Systems in the z-Domain193

3.5.1 Response of Systems with Rational System Functions194

3.5.2 Transient and Steady-State Responses195

3.5.3 Causality and Stability196

3.5.4 Pole-Zero Cancellations198

3.5.5 Multiple-Order Poles and Stability200

3.5.6 Stability of Second-Order Systems201

3.6 The One-sided z-Transform205

3.6.1 Definition and Properties206

3.6.2 Solution of Difference Equations210

3.6.3 Response of Pole-Zero Systems with Nonzer0 Initial Conditions211

3.7 Summary and References214

Problems214

4 Frequency Analysis of Signals224

4.1 Frequency Analysis of Continuous-Time Signals225

4.1.1 The Fourier Series for Continuous-Time Periodic Signals226

4.1.2 Power Density Spectrum of Periodic Signals230

4.1.3 The Fourier Transform for Continuous-Time Aperiodic Signals234

4.1.4 Energy Density Spectrum of Aperiodic Signals238

4.2 Frequency Analysis of Discrete-Time Signals241

4.2.1 The Fourier Series for Discrete-Time Periodic Signals241

4.2.2 Power Density Spectrum of Periodic Signals245

4.2.3 The Fourier Transform of Discrete-Time Aperiodic Signals248

4.2.4 Convergence of the Fourier Transform251

4.2.5 Energy Density Spectrum of Aperiodic Signals254

4.2.6 Relationship of the Fourier Transform to the z-Transform259

4.2.7 TheCepstrum261

4.2.8 The Fourier Transform of Signals with Poles on the Unit Circle262

4.2.9 Frequency-Domain Classification of Signals: The Concept of Bandwidth265

4.2.10 The Frequency Ranges of Some Natural Signals267

4.3 Frequency-Domain and Time-Domain Signal Properties268

4.4 Properties of the Fourier Transform for Discrete-Time Signals271

4.4.1 Symmetry Properties of the Fourier Transform272

4.4.2 Fourier Transform Theorems and Properties279

4.5 Summary and References291

Problems292

5 Frequency-Domain Analysis of LTI Systems300

5.1 Frequency-Domain Characteristics of Linear Time-Invariant Systems300

5.1.1 Response to Complex Exponential and Sinusoidal Signals: The Frequency Response Function301

5.1.2 Steady-State and Transient Response to Sinusoidal Input Signals310

5.1.3 Steady-State Response to Periodic Input Signals311

5.1.4 Response to Aperiodic Input Signals312

5.2 Frequency Response of LTI Systems314

5.2.1 Frequency Response of a System with a Rational System Function314

5.2.2 Computation of the Frequency Response Function317

5.3 Correlation Functions and Spectra at the Output of LTI Systems321

5.3.1 Input-Output Correlation Functions and Spectra322

5.3.2 Correlation Functions and Power Spectra for Random Input Signals323

5.4 Linear Time-Invariant Systems as Frequency-Selective Filters326

5.4.1 Ideal Filter Characteristics327

5.4.2 Lowpass, Highpass, and Bandpass Filters329

5.4.3 Digital Resonators335

5.4.4 Notch Filters339

5.4.5 Comb Filters341

5.4.6 All-Pass Filters345

5.4.7 Digital Sinusoidal Oscillators347

5.5 Inverse Systems and Deconvolution349

5.5.1 Invertibility of Linear Time-Invariant Systems350

5.5.2 Minimum-Phase, Maximum-Phase, and Mixed-Phase Systems354

5.5.3 System Identification and Deconvolution358

5.5.4 Homomorphic Deconvolution360

5.6 Summary and References362

Problems363

6 Sampling and Reconstruction of Signals384

6.1 Ideal Sampling and Reconstruction of Continuous-Time Signals384

6.2 Discrete-Time Processing of Continuous-Time Signals395

6.3 Analog-to-Digital and Digital-to-Analog Converters401

6.3.1 Analog-to-Digital Converters401

6.3.2 Quantization and Coding403

6.3.3 Analysis of Quantization Errors406

6.3.4 Digital-to-Analog Converters408

6.4 Sampling and Reconstruction of Continuous-Time Bandpass Signals410

6.4.1 Uniform or First-Order Sampling411

6.4.2 Interleaved or Nonuniform Second-Order Sampling416

6.4.3 Bandpass Signal Representations422

6.4.4 Sampling Using Bandpass Signal Representations426

6.5 Sampling of Discrete-Time Signals427

6.5.1 Sampling and Interpolation of Discrete-Time Signals427

6.5.2 Representation and Sampling of Bandpass Discrete-Time Signals430

6.6 Oversampling A/D and D/A Converters433

6.6.1 Oversampling A/D Converters433

6.6.2 Oversampling D/A Converters439

6.7 Summary and References440

Problems440

7 The Discrete Fourier Transform: Its Properties and Applications449

7.1 Frequency-Domain Sampling: The Discrete Fourier Transform449

7.1.1 Frequency-Domain Sampling and Reconstruction of Discrete-Time Signals449

7.1.2 The Discrete Fourier Transform (DFT)454

7.1.3 The DFT as a Linear Transformation459

7.1.4 Relationship of the DFT to Other Transforms461

7.2 Properties of the DFT464

7.2.1 Periodicity, Linearity, and Symmetry Properties465

7.2.2 Multiplication of Two DFTs and Circular Convolution471

7.2.3 Additional DFT Properties476

7.3 Linear Filtering Methods Based on the DFT480

7.3.1 Use of the DFT in Linear Filtering481

7.3.2 Filtering of Long Data Sequences485

7.4 Frequency Analysis of Signals Using the DFT488

7.5 The Discrete Cosine Transform495

7.5.1 Forward DCT495

7.5.2 Inverse DCT497

7.5.3 DCT as an Orthogonal Transform498

7.6 Summary and References501

Problems502

8 Efficient Computation of the DFT: Fast Fourier Transform Algorithms511

8.1 Efficient Computation of the DFT: FFT Algorithms511

8.1.1 Direct Computation of the DFT512

8.1.2 Divide-and-Conquer Approach to Computation of the DFT513

8.1.3 Radix-2 FFT Algorithms519

8.1.4 Radix-4 FFT Algorithms527

8.1.5 Split-Radix FFT Algorithms532

8.1.6 Implementation of FFT Algorithms536

8.2 Applications of FFT Algorithms538

8.2.1 Efficient Computation of the DFT of Two Real Sequences538

8.2.2 Efficient Computation of the DFT of a 2N-Point Real Sequence539

8.2.3 Use of the FFT Algorithm in Linear Filtering and Correlation540

8.3 A Linear Filtering Approach to Computation of the DFT542

8.3.1 The Goertzel Algorithm542

8.3.2 The Chirp-z Transform Algorithm544

8.4 Quantization Effects in the Computation of the DFT549

8.4.1 Quantization Errors in the Direct Computation of the DFT549

8.4.2 Quantization Errors in FFT Algorithms552

8.5 Summary and References555

Problems556

9 Implementation of Discrete-Time Systems563

9.1 Structures for the Realization of Discrete-Time Systems563

9.2 Structures for FIR Systems565

9.2.1 Direct-Form Structure566

9.2.2 Cascade-Form Structures567

9.2.3 Frequency-Sampling Structures569

9.2.4 Lattice Structure574

9.3 Structures for IIR Systems582

9.3.1 Direct-Form Structures582

9.3.2 Signal Flow Graphs and Transposed Structures585

9.3.3 Cascade-Form Structures589

9.3.4 Parallel-Form Structures591

9.3.5 Lattice and Lattice-Ladder Structures for IIR Systems594

9.4 Representation of Numbers601

9.4.1 Fixed-Point Representation of Numbers601

9.4.2 Binary Floating-Point Representation of Numbers605

9.4.3 Errors Resulting from Rounding and Truncation608

9.5 Quantization of Filter Coefficients613

9.5.1 Analysis of Sensitivity to Quantization of Filter Coefficients613

9.5.2 Quantization of Coefficients in FIR Filters620

9.6 Round-Off Effects in Digital Filters624

9.6.1 Limit-Cycle Oscillations in Recursive Systems624

9.6.2 Scaling to Prevent Overflow629

9.6.3 Statistical Characterization of Quantization Effects in Fixed-Point Realizations of Digital Filters631

9.7 Summary and References640

Problems641

10 Design of Digital Filters654

10.1 General Considerations654

10.1.1 Causality and Its Implications655

10.1.2 Characteristics of Practical Frequency-Selective Filters659

10.2 Design of FIR Filters660

10.2.1 Symmetric and Antisymmetric FIR Filters660

10.2.2 Design of Linear-Phase FIR Filters Using Windows664

10.2.3 Design of Linear-Phase FIR Filters by the Frequency-Sampling Method671

10.2.4 Design of Optimum Equiripple Linear-Phase FIR Filters678

10.2.5 Design of FIR Differentiators691

10.2.6 Design of Hilbert Transformers693

10.2.7 Comparison of Design Methods for Linear-Phase FIR Filters700

10.3 Design of IIR Filters From Analog Filters701

10.3.1 IIR Filter Design by Approximation of Derivatives703

10.3.2 IIR Filter Design by Impulse Invariance707

10.3.3 IIR Filter Design by the Bilinear Transformation712

10.3.4 Characteristics of Commonly Used Analog Filters717

10.3.5 Some Examples of Digital Filter Designs Based on the Bilinear Transformation727

10.4 Frequency Transformations730

10.4.1 Frequency Transformations in the Analog Domain730

10.4.2 Frequency Transformations in the Digital Domain732

10.5 Summary and References734

Problems735

11 Multirate Digital Signal Processing750

11.1 Introduction751

11.2 Decimation by a Factor D755

11.3 Interpolation by a Factor I760

11.4 Sampling Rate Conversion by a Rational Factor I/D762

11.5 Implementation of Sampling Rate Conversion766

11.5.1 Polyphase Filter Structures766

11.5.2 Interchange of Filters and Downsamplers/Upsamplers767

11.5.3 Sampling Rate Conversion with Cascaded Integrator Comb Filters769

11.5.4 Polyphase Structures for Decimation and Interpolation Filters771

11.5.5 Structures for Rational Sampling Rate Conversion774

11.6 Multistage Implementation of Sampling Rate Conversion775

11.7 Sampling Rate Conversion of Bandpass Signals779

11.8 Sampling Rate Conversion by an Arbitrary Factor781

11.8.1 Arbitrary Resampling with Polyphase Interpolators782

11.8.2 Arbitrary Resampling with Farrow Filter Structures782

11.9 Applications of Multirate Signal Processing784

11.9.1 Design of Phase Shifters784

11.9.2 Interfacing of Digital Systems with Different Sampling Rates785

11.9.3 Implementation of Narrowband Lowpass Filters786

11.9.4 Subband Coding of Speech Signals787

11.10 Digital Filter Banks790

11.10.1 Polyphase Structures of Uniform Filter Banks794

11.10.2 Transmultiplexers796

11.11 Two-Channel Quadrature Mirror Filter Bank798

11.11.1 Elimination of Aliasing799

11.11.2 Condition for Perfect Reconstruction801

11.11.3 Polyphase Form of the QMF Bank801

11.11.4 Linear Phase FIR QMF Bank802

11.11.5 IIR QMF Bank803

11.11.6 Perfect Reconstruction Two-Channel FIR QMF Bank803

11.11.7 Two-Channel QMF Banks in Subband Coding806

11.12 A/-Channel QMF Bank807

11.12.1 Alias-Free and Perfect Reconstruction Condition808

11.12.2 Polyphase Form of the M-Channel QMF Bank808

11.13 Summary and References813

Problems813

12 Linear Prediction and Optimum Linear Filters823

12.1 Random Signals, Correlation Functions, and Power Spectra823

12.1.1 Random Processes824

12.1.2 Stationary Random Processes825

12.1.3 Statistical (Ensemble) Averages825

12.1.4 Statistical Averages for Joint Random Processes826

12.1.5 Power Density Spectrum828

12.1.6 Discrete-Time Random Signals829

12.1.7 Time Averages for a Discrete-Time Random Process830

12.1.8 Mean-Ergodic Process831

12.1.9 Correlation-Ergodic Processes832

12.2 Innovations Representation of a Stationary Random Process834

12.2.1 Rational Power Spectra836

12.2.2 Relationships Between the Filter Parameters and the Autocorrelation Sequence837

12.3 Forward and Backward Linear Prediction838

12.3.1 Forward Linear Prediction839

12.3.2 Backward Linear Prediction841

12.3.3 The Optimum Reflection Coefficients for the Lattice Forward and Backward Predictors845

12.3.4 Relationship of an AR Process to Linear Prediction846

12.4 Solution of the Normal Equations846

12.4.1 The Levinson-Durbin Algorithm847

12.4.2 The Schur Algorithm850

12.5 Properties of the Linear Prediction-Error Filters855

12.6 AR Lattice and ARMA Lattice-Ladder Filters858

12.6.1 AR Lattice Structure858

12.6.2 ARMA Processes and Lattice-Ladder Filters860

12.7 Wiener Filters for Filtering and Prediction863

12.7.1 FIR Wiener Filter864

12.7.2 Orthogonality Principle in Linear Mean-Square Estimation866

12.7.3 IIR Wiener Filter867

12.7.4 Noncausal Wiener Filter872

12.8 Summary and References873

Problems874

13 Adaptive Filters880

13.1 Applications of Adaptive Filters880

13.1.1 System Identification or System Modeling882

13.1.2 Adaptive Channel Equalization883

13.1.3 Echo Cancellation in Data Transmission over Telephone Channels887

13.1.4 Suppression of Narrowband Interference in a Wideband Signal891

13.1.5 Adaptive Line Enhancer895

13.1.6 Adaptive Noise Cancelling896

13.1.7 Linear Predictive Coding of Speech Signals897

13.1.8 Adaptive Arrays900

13.2 Adaptive Direct-Form FIR Filters--The LMS Algorithm902

13.2.1 Minimum Mean-Square-Error Criterion903

13.2.2 The LMS Algorithm905

13.2.3 Related Stochastic Gradient Algorithms907

13.2.4 Properties of the LMS Algorithm909

13.3 Adaptive Direct-Form Filters--RLS Algorithms916

13.3.1 RLS Algorithm916

13.3.2 The LDU Factorization and Square-Root Algorithms921

13.3.3 Fast RLS Algorithms923

13.3.4 Properties of the Direct-Form RLS Algorithms925

13.4 Adaptive Lattice-Ladder Filters927

13.4.1 Recursive Least-Squares Lattice-Ladder Algorithms928

13.4.2 Other Lattice Algorithms949

13.4.3 Properties of Lattice-Ladder Algorithms950

13.5 Summary and References954

Problems955

14 Power Spectrum Estimation960

14.1 Estimation of Spectra from Finite-Duration Observations of Signals961

14.1.1 Computation of the Energy Density Spectrum961

14.1.2 Estimation of the Autocorrelation and Power Spectrum of Random Signals: The Periodogram966

14.1.3 The Use of the DFT in Power Spectrum Estimation971

14.2 Nonparametric Methods for Power Spectrum Estimation974

14.2.1 The Bartlett Method: Averaging Periodograms974

14.2.2 The Welch Method: Averaging Modified Periodograms975

14.2.3 The Blackman and Tukey Method: Smoothing the Periodogram978

14.2.4 Performance Characteristics of Nonparametric Power Spectrum Estimators981

14.2.5 Computational Requirements of Nonparametric Power Spectrum Estimates984

14.3 Parametric Methods for Power Spectrum Estimation986

14.3.1 Relationships Between the Autocorrelation and the Model Parameters988

14.3.2 The Yule-Walker Method for the AR Model Parameters990

14.3.3 The Burg Method for the AR Model Parameters991

14.3.4 Unconstrained Least-Squares Method for the AR Model Parameters994

14.3.5 Sequential Estimation Methods for the AR Model Parameters995

14.3.6 Selection of AR Model Order996

14.3.7 MA Model for Power Spectrum Estimation997

14.3.8 ARM A Model for Power Spectrum Estimation999

14.3.9 Some Experimental Results1001

14.4 Filter Bank Methods1009

14.4.1 Filter Bank Realization of the Periodogram1010

14.4.2 Minimum Variance Spectral Estimates1012

14.5 Eigenanalysis Algorithms for Spectrum Estimation1015

14.5.1 Pisarenko Harmonic Decomposition Method1017

14.5.2 Eigen-decomposition of the Autocorrelation Matrix for Sinusoids in White Noise1019

14.5.3 MUSIC Algorithm1021

14.5.4 ESPRIT Algorithm1022

14.5.5 Order Selection Criteria1025

14.5.6 Experimental Results1026

14.6 Summary and References1029

Problems1030

A Random Number Generators1041

B Tables of Transition Coefficients for the Design of Linear-Phase FIR Filters1047

References and Bibliography1053

Answers to Selected Problems1067

Index1077