离散时间信号处理 第2版PDF|Epub|txt|kindle电子书版本网盘下载

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1 INTRODUCTION1

2DISCRETE-TIME SIGNALS AND SYSTEMS8

2.0 Introduction8

2.1 Discrete-Time Signals: Sequences9

2.1.1 Basic Sequences and Sequence Operations11

2.2 Discrete-Time Systems16

2.2.1 Memoryless Systems18

2.2.2 Linear Systems18

2.2.3 Time-Invariant Systems20

2.2.4 Causality21

2.2.5 Stability21

2.3 Linear Time-Invariant Systems22

2.4 Properties of Linear Time-Invariant Systems28

2.5 Linear Constant-Coefficient Difference Equations34

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 Propertiesof the Fourier Transform55

2.9 Fourier Transform Theorems58

2.9.1 Linearity of the Fourier Transform59

2.9.2 Time Shifting and Frequency Shifting59

2.9.3 Time Reversal60

2.9.4 Differentiation in Frequency60

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 Signals65

2.11 Summary70

Problems70

3THE Z-TRANSFORM94

3.0 Introduction94

3.1 z-Transform94

3.2 Properties of the Region of Convergence for the z-Transform105

3.3 The Inverse z-Transform111

3.3.1 Inspection Method111

3.3.2 Partial Fraction Expansion112

3.3.3 Power Series Expansion116

3.4 z-Transform Properties119

3.4.1 Linearity119

3.4.2 Time Shifting120

3.4.3 Multiplication by an Exponential Sequence121

3.4.4 Differentiation of X（z ）122

3.4.5 Conjugation of a Complex Sequence123

3.4.6 Time Reversal123

3.4.7 Convolution of Sequences124

3.4.8 Initial-Value Theorem126

3.4.9 Summary of Some z-Transform Properties126

3.5 Summary126

Problems127

4SAMPLING OF CONTINUOUS-TIME SIGNALS140

4.0 Introduction140

4.1 Periodic Sampling140

4.2 Frequency-Domain Representation of Sampling142

4.3 Reconstruction of a Bandlimited Signal from Its Samples150

4.4 Discrete-Time Processing of Continuous-Time Signals153

4.4.1 Linear Time-Invariant Discrete-Time Systems154

4.4.2 Impulse Invariance160

4.5 Continuous-Time Processing of Discrete-Time Signals163

4.6 Changing the Sampling Rate Using Discrete-Time Processing167

4.6.1 Sampling Rate Reduction by an Integer Factor167

4.6.2 Increasing the Sampling Rate by an Integer Factor172

4.6.3 Changing the Sampling Rate by a Noninteger Factor176

4.7 Multirate Signal Processing179

4.7.1 Interchange of Filtering and Downsampling/Upsampling179

4.7.2 Polyphase Decompositions180

4.7.3 Polyphase Implementation of Decimation Filters182

4.7.4 Polyphase Implementation of Interpolation Filters183

4.8 Digital Processing of Analog Signals185

4.8.1 Prefiltering to Avoid Aliasing185

4.8.2 Analog-to-Digital （A/D） Conversion187

4.8.3 Analysis of Quantization Errors193

4.8.4 D/A Conversion197

4.9 Oversampling and Noise Shaping in A/D and D/A Conversion201

4.9.1 Oversampled A/D Conversion with DirectQuantization201

4.9.2 Oversampled A/D Conversion with Noise Shaping206

4.9.3 Oversampling and Noise Shaping in D/A Conversion210

4.10 Summary213

Problems214

5 TRANSFORM ANALYSIS OF LINEAR TIME-INVARIANT SYSTEMS240

5.0 Introduction240

5.1 The Frequency Response of LTI Systems241

5.1.1 Ideal Frequency-Selective Filters241

5.1.2 Phase Distortion and Delay242

5.2 System Functions for Systems Characterized by Linear Constant-Coefficient Difference Equations245

5.2.1 Stability and Causality247

5.2.2 Inverse Systems248

5.2.3 Impulse Response for Rational System Functions250

5.3 Frequency Response for Rational System Functions253

5.3.1 Frequency Response of a Single Zero or Pole258

5.3.2 Examples with Multiple Poles and Zeros265

5.4 Relationship between Magnitude and Phase270

5.5 All-Pass Systems274

5.6 Minimum-Phase Systems280

5.6.1 Minimum-Phase and All-Pass Decomposition280

5.6.2 Frequency-Response Compensation282

5.6.3 Properties of Minimum-Phase Systems287

5.7 Linear Systems with Generalized Linear Phase291

5.7.1 Systems with Linear Phase292

5.7.2 Generalized Linear Phase295

5.7.3 Causal Generalized Linear-Phase Systems297

5.7.4 Relation of FIR Linear-Phase Systems to Minimum-Phase Systems308

5.8 Summary311

Problems312

6STRUCTURES FOR DISCRETE-TIME SYSTEMS340

6.0 Introduction340

6.1 Block Diagram Representation of Linear Constant-Coefficient Difference Equations341

6.2 Signal Flow Graph Representation of Linear Constant-Coefficient Difference Equations348

6.3 Basic Structures for IIR Systems354

6.3.1 Direct Forms354

6.3.2 Cascade Form356

6.3.3 Parallel Form359

6.3.4 Feedback in IIR Systems361

6.4 Transposed Forms363

6.5 Basic Network Structures for FIR Systems366

6.5.1 Direct Form367

6.5.2 Cascade Form367

6.5.3 Structures for Linear-Phase FIR Systems368

6.6 Overview of Finite-Precision Numerical Effects370

6.6.1 Number Representations371

6.6.2 Quantization in Implementing Systems374

6.7 The Effects of Coeffiicient Quantization377

6.7.1 Effects of Coefficient Quantization in IIR Systems377

6.7.2 Example of Coefficient Quantization in an Elliptic Filter379

6.7.3 Poles of Quantized Second-Order Sections382

6.7.4 Effects of Coefficient Quantization in FIR Systems384

6.7.5 Example of Quantization of an Optimum FIR Filter386

6.7.6 Maintaining Linear Phase390

6.8 Effects of Round-off Noise in Digital Filters391

6.8.1 Analysis of the Direct-Form IIR Structures391

6.8.2 Scaling in Fixed-Point Implementations of IIR Systems399

6.8.3 Example of Analysis of a Cascade IIR Structure403

6.8.4 Analysis of Direct-Form FIR Systems410

6.8.5 Floating-Point Realizations of Discrete-Time Systems412

6.9 Zero-Input Limit Cycles in Fixed-Point Realizations of IIR Digital Filters413

6.9.1 Limit Cycles due to Round-off and Truncation414

6.9.2 Limit Cycles Due to Overflow416

6.9.3 Avoiding Limit Cycles417

6.10 Summary418

7Problems 419FILTER DESIGN TECHNIQUES439

7.0 Introduction439

7.1 Design of Discrete-Time IIR Filters from Continuous-TimeFilters442

7.1.1 Filter Design by Impulse Invariance443

7.1.2 Bilinear Transformation450

7.1.3.Examples of Bilinear Transformation Design454

7.2 Design of FIR Filters by Windowing465

7.2.1 Properties of Commonly Used Windows467

7.2.2 Incorporation of Generalized Linear Phase469

7.2.3 The Kaiser Window Filter Design Method474

7.2.4 Relationship of the Kaiser Windowto Other Windows478

7.3 Examples of FIR Filter Design by the Kaiser Window Method478

7.3.1 Highpass Filter479

7.3.2 Discrete-Time Differentiators482

7.4 Optimum Approximations of FIR Filters486

7.4.1 Optimal Type Ⅰ Lowpass Filters491

7.4.2 Optimal Type Ⅱ Lowpass Filters497

7.4.3 The Parks-McClellan Algorithm498

7.4.4 Characteristics of Optimum FIR Filters501

7.5 Examples of FIR Equiripple Approximation503

7.5.1 Lowpass Filter503

7.5.2 Compensation for Zero-Order Hold506

7.5.3 Bandpass Filter507

7.6 Comments on IIR and FIR Discrete-Time Filters510

7.7 Summary511

Problems511

8THE DISCRETE FOURIER TRANSFORM541

8.0 Introduction541

8.1 Representation of PeriodicSequences: The Discrete FourierSeries542

8.2 Properties of the Discrete Fourier Series546

8.2.1 Linearity546

8.2.2 Shift of a Sequence546

8.2.3 Duality547

8.2.4 Symmetry Properties547

8.2.5 Periodic Convolution548

8.2.6 Summary of Properties of the DFS Representation of PeriodicSequences550

8.3 The Fourier Transform of Periodic Signals551

8.4 Sampling the Fourier Transform555

8.5 Fourier Representation of Finite-Duration Sequences: The DiscreteFourier Transform559

8.6 Properties of the Discrete Fourier Transform564

8.6.1 Linearity564

8.6.2 Circular Shift of a Sequence564

8.6.3 Duality567

8.6.4 Symmetry Properties568

8.6.5 Circular Convolution571

8.6.6 Summary of Properties of the Discrete Fourier Transform575

8.7 Linear Convolution Using the Discrete Fourier Transform576

8.7.1 Linear Convolution of Two Finite-Length Sequences577

8.7.2 Circular Convolution as Linear Convolution with Aliasing577

8.7.3 Implementing Linear Time-Invariant Systems Using theDFT582

8.8 The Discrete Cosine Transform （DCT）589

8.8.1 Definitions of the DCT589

8.8.2 Definition of the DCT-1 and DCT-2590

8.8.3 Relationship between the DFT and the DCT-1593

8.8.4 Relationship between the DFT and the DCT-2594

8.8.5 Energy Compaction Property of the DCT-2595

8.8.6 Applications of the DCT598

8.9 Summary599

Problems600

9 COMPUTATION OF THE DISCRETE FOURIERTRANSFORM629

9.0 Introduction629

9.1 Efficient Computation of the Discrete Fourier Transform630

9.2 The Goertzel Algorithm633

9.3 Decimation-in-Time FFT Algorithms635

9.3.1 In-Place Computations640

9.3.2 Alternative Forms643

9.4 Decimation-in-Frequency FFT Algorithms646

9.4.1 In-Place Computation650

9.4.2 Alternative Forms650

9.5 Practical Considerations652

9.5.1 Indexing652

9.5.2 Coefficients654

9.5.3 Algorithms for More General Values of N655

9.6 Implementation of the DFT Using Convolution655

9.6.1 Overview of the Winograd Fourier Transform Algorithm655

9.6.2 The Chirp Transform Algorithm656

9.7 Effects of Finite Register Length661

9.8 Summary669

Problems669

10 FOURIER ANALYSIS OF SIGNALS USING THE DISCRETE FOURIER TRANSFORM693

10.0 Introduction693

10.1 Fourier Analysis of Signals Using the DFT694

10.2 DFT Analysis of Sinusoidal Signals697

10.2.1 The Effect of Windowing698

10.2.2 The Effect of Spectral Sampling703

10.3 The Time-Dependent Fourier Transform714

10.3.1 The Effect of the Window717

10.3.2 Sampling in Time and Frequency718

10.4 Block Convolution Using the Time-Dependent Fourier Transform722

10.5 Fourier Analysis of Nonstationary Signals723

10.5.1 Time-Dependent Fourier Analysis of Speech Signals724

10.5.2 Time-Dependent Fourier Analysis of Radar Signals728

10.6 Fourier Analysis of Stationary Random Signals: The Periodogram730

10.6.1 The Periodogram731

10.6.2 Properties of the Periodogram733

10.6.3 Periodogram Averaging737

10.6.4 Computation of Average Periodograms Using the DFT739

10.6.5 An Example of Periodogram Analysis739

10.7 Spectrum Analysis of Random Signals Using Estimates of theAutocorrelation Sequence743

10.7.1 Computing Correlation and Power Spectrum Estimates Usingthe DFT746

10.7.2 An Example of Power Spectrum Estimation Based onEstimation of the Autocorrelation Sequence748

10.8 Summary754

Problems755

11DISCRETE HILBERT TRANSFORMS775

11.0 Introduction775

11.1 Real- and Imaginary-Part Sufficiency of the Fourier Transform forCausal Sequences777

11.2 Sufficiency Theorems for Finite-Length Sequences782

11.3 Relationships Between Magnitude and Phase788

11.4 Hilbert Transform Relations for Complex Sequences789

11.4.1 Design of Hilbert Transformers792

11.4.2 Representation of Bandpass Signals796

11.4.3 Bandpass Sampling799

11.5 Summary801

Problems802

APPENDIX A RANDOM SIGNALS811

A.1 Discrete-Time Random Processes811

A.2 Averages813

A.2.1 Definitions813

A.2.2 Time Averages815

A.3 Properties of Correlation and Covariance Sequences817

A.4 Fourier Transform Representation of Random Signals818

A.5 Use of the z-Transform in Average Power Computations820

APPENDIX B CONTINUOUS-TIME FILTERS824

B.1 Butterworth Lowpass Filters824

B.2 Chebyshev Filters826

B.3 Elliptic Filters828

APPENDIX C ANSWERS TO SELECTED BASICPROBLEMS830

BIBLIOGRAPHY851

INDEX859