Discrete-time signal processing【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

Discrete-time signal processingPDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

1 INTRODUCTION1

2 DISCRETE-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 Properties of 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

3 THE 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

4 SAMPLING 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 and Integer Factor167

4.6.2 Increasing the Sampling Rate by and 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 Dccompositions180

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 Direct Quantization201

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

6 STRUCTURES 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 Coefficient 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 Caseade 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

Problems419

7 FILTER DESIGN TECHNIQUES439

7.0 Introduction439

7.1 Design of Discrete-Time IIR Filters from Continuous-Time Filters442

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 Window to Other Windows478

7.3 Examples of FIR Filter Design by the Kaiser Window Method478

7.3.1 Highpass Filter479

7.3.2 Discrete-Time Differentiatiors482

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

8 THE DISCRETE FOURIER TRANSFORM541

8.0 Introduction541

8.1 Representation of Periodic Sequences: The Discrete Fourier Series542

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 Periodic Sequences550

8.3 The Fourier Transform of Periodic Signals551

8.4 Sampling the Fourier Transform555

8.5 Fourier Representation of Finite-Duration Sequences: The Discrete Fourier 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 the DFT582

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 Application of the DCT598

8.9 Summary599

Problems600

9 COMPUTATION OF THE DISCRETE FOURIER TRANSFORM629

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 the Autocorrelation Sequence743

10.7.1 Computing Correlation and Power Spectrum Estimates Using the DFT746

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

10.8 Summary754

Problems755

11 DISCRETE HILBERT TRANSFORMS775

11.0 Introduction775

11.1 Real-and Imaginary-Part Sufficiency of the Fourier Transform for Causal 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 BASIC PROBLEMS830

BIBLIOGRAPHY851

INDEX859

Example2.1 Combining Basic Sequences13

Example2.2 Periodic and Aperiodic Discrete-Time Sinusoids15

Example2.3 The Ideal Delay System17

Example2.4 Moving Average17

Example2.5 A Memoryless System18

Example2.6 The Accumulator System19

Example2.7 A Nonlinear System19

Example2.8 The Accumulator as a Time-Invariant System20

Example2.9 The Compressor System20

Example2.10 The Forward and Backward Difference Systems21

Example2.11 Testing for Stability or Instability22

Example2.12 Computation of the Convolution Sum25

Example2.13 Analytical Evaluation of the Convolution Sum26

Example2.14 Difference Equation Representation of the Accumulator34

Example2.15 Differentce Equation Representation of the Moving-Average Systgem35

Example2.16 Recursive Computation of Difference Equations37

Example2.17 Frequency Response of the Ideal Delay System41

Example2.18 Sinusoidal Response of LTI Systems42

Example2.19 Ideal Frequency-Selective Filters43

Example2.20 Frequency Response of the Moving-Average System44

Example2.21 Absolute Summability for a Suddenly-Applied Exponential51

Example2.22 Square-Summability for the Ideal Lowpass Filter52

Example2.23 Fourier Transform of a Constant53

Example2.24 Fourier Transform of Complex Exponential Sequences54

Example2.25 Illustration of Symmetry Properties57

Example2.26 Determining a Fourier Transform Using Tables 2.2 and 2.363

Example2.27 Determining an Inverse Fourier Transform Using Tables 2.2 and 2.363

Example2.28 Determining the Impulse Response from the Frequency Response64

Example2.29 Determining the Impulse Response for a Difference Equation64

Example2.30 White Noise69

Example3.1 Right-Sided Exponential Sequence98

Example3.2 Left-Sided Exponential Sequence99

Example3.3 Sum of Two Exponential Sequences100

Example3.4 Sum of Two Exponentials (Again)101

Example3.5 Two-Sided Exponential Sequence102

Example3.6 Finite-Length Sequence103

Example3.7 Stability, Causality, and the ROC110

Example3.8 Second-Order z-Transform113

Example3.9 Inverse by Partial Fractions115

Example3.10 Finite-Length Sequence117

Example3.11 Inverse Transform by Power Series Expansion117

Example3.12 Power Series Expansion by Long Division118

Example3.13 Power Series Expansion for a Left-Sided Sequence118

Example3.14 Shifted Exponential Sequence120

Example3.15 Exponential Multiplication121

Example3.16 Inverse of Non-Rational z-Transform122

Example3.17 Second-Order Pole123

Example3.18 Time-Reversed Exponential Sequence124

Example3.19 Evaluating a Convolution Using the z-Transform125

Example4.1 Sampling and Reconstruction of a Sinusoidal Signal147

Example4.2 Aliasing in the Reconstruction of an Undersampled Sinusoidal Signal148

Example4.3 A Second Example of Aliasing149

Example4.4 Ideal Continuous-Time Lowpass Filtering Using a Discrete-Time Lowpass Filter155

Example4.5 Discrete-Time Implementation of an Ideal Continuous-Time Bandlimited Differentiator158

Example4.6 Illustration of Example 4.5 with a Sinusoidal Input159

Example4.7 A Discrete-Time Lowpass Filter Obtained By Impulse Invariance162

Example4.8 Impulse Invariance Applied to Continuous-Time Systems with Rational System Functions162

Example4.9 Noninteger Delay164

Example4.10 Moving-Average System with Noninteger Delay165

Example4.11 SamplingRate Conversion by a Noninteger Rational Factor177

Example4.12 Quantization Error For a Sinusoidal Signal194

Example5.1 Effects of Attenuation and Group Delay243

Example5.2 Second-Order System246

Example5.3 Determining the ROC247

Example5.4 Inverse System for First-Order System249

Example5.5 Inverse for System with a Zero in the ROC250

Example5.6 A First-Order IIR System251

Example5.7 A Simple FIR System252

Example5.8 Second-Order IIR System265

Example5.9 Second-Order FIR System268

Example5.10 Third-Order IIR System268

Example5.11 Systems with the Same C (z)271

Example5.13 First-and Second-Order All-Pass Systems275

Example5.14 Minimum-Phase/All-Pass Decomposition281

Example5.15 Compensation of an FIR System283

Example5.16 Ideal Lowpass with Linear Phase293

Example5.17 Type I Linear-Phase System300

Example5.18 Type II Linear-Phase System302

Example5.19 Type III Linear-Phase System302

Example5.20 Type IV Linear-Phase System302

Example5.21 Decomposition of a Linear-Phase System308

Example6.1 Block Diagram Representation of a Difference Equation342

Example6.2 Direct Form I and Direct Form II Implementation of and LTI System347

Example6.3 Determination of the System Function from a Flow Graph352

Example6.4 Illustration of Direct Form I and Direct Form II Structures355

Example6.5 Illustration of Cascade Structures358

Example6.6 Illustration of Parallel-Form Structures360

Example6.7 Transposed Form for a First-Order System with No Zeroes363

Example6.8 Transposed Form for a Basic Second-Order Section364

Example6.9 Round-Off Noise in a First-Order System396

Example6.10 Round-Off Noise in a Second-Order System397

Example6.11 Interaction Between Scaling and Round-off Noise402

Example6.12 Scaling Considerations for the FIR System in Section 6.7.5411

Example6.13 Limit Cycle Behavior in a First-Order System414

Example6.14 Overflow Oscillations in a Second-Order System416

Example7.1 Determining Specifications for a Discrete-Time Filter440

Example7.2 Impulse Invariance with a Butterworth Filter446

Example7.3 Bilinear Transformation of a Butterworth Filter454

Example7.4 Butterworth Approximation458

Example7.5 Chebyshev Approximation460

Example7.6 Elliptic Approximation463

Example7.7 Linear-Phase Lowpass Filter472

Example7.8 Kaiser Window Design of a Lowpass Filter476

Example7.9 Kaiser Window Design of a Hisghpass Filter479

Example7.10 Kaiser Window Design of a Differentiator483

Example7.11 Alternation Theorem and Polynomials490

Example8.1 Discrete Fourier Series of a Periodic Impulse Train544

Example8.2 Duality in the Discrete Fourier Series544

Example8.3 The Discrete Fourier Series of a Periodic Rectangular Pulse Train545

Example8.4 Periodic Convolution549

Example8.5 The Fourier Transform of a Periodic Impulse Train552

Example8.6 Relationship Between the Fourier Series Coefficients and the Fourier Transform of One Period554

Example8.7 The DFT of a Rectangular Pulse561

Example8.8 Circular Shift of a Sequence566

Example8.9 The Duality Relationship for the DFT568

Example8.10 Circular Convolution with a Delayed Impulse Sequence572

Example8.11 Circular Convolution of Two Rectangular Pulses573

Example8.12 Circular Convolution as Linear Convolution with Aliasing579

Example8.13 Energy Compaction in the DCT-2596

Example9.1 Chirp Transform Parameters661

Example10.1 Fourier Analysis Using the DFT697

Example10.2 Relationship Between DFT Values697

Example10.3 Effcct of Windowing on Fourier Analysis of Sinusoidal Signals698

Example10.4 Illustration of the Effect of Spectral Sampling703

Example10.5 Spectral Sampling with Frequencies Matching DFT Frequencies706

Example10.6 DFT Analysis of Sinusoidal Signals Using a Kaiser Window708

Example10.7 DFT Analysis with 32-point Kaiser Window and Zero-Padding711

Example10.8 Oversampling and Linear Interpolation for Frequency Estimation713

Example10.9 Time-Dependent Fourier Transform of a Linear Chirp Signal715

Example10.10 Spectrogram Display of the Time-Dependent Fourier Transform of Speech725

Example11.1 Finite-Length Sequence779

Example11.2 Exponential Sequence779

Example11.3 Periodic Sequence787

Example11.4 Kaiser Window Design of Hilbert Transformers793

ExampleA.1 Noise Power Output of Ideal Lowpass Filter820

ExampleA.2 Noise Power Output of a Second-Order IIR Filter823