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Discrete-Time Signal Processing

by: Oppenheim, Alan V.; Schafer, Ronald W.

Discrete-Time Signal Processing

by: Oppenheim, Alan V.; Schafer, Ronald W.

ISBN 13:
9780137549207
ISBN 10:
0137549202
Edition: 2nd
Format: Hardcover
Copyright: 01/01/2010
Publisher: Prentice Hall
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Summary

For senior/graduate-level courses in Discrete-Time Signal Processing. THE definitive, authoritative text on DSP - ideal for those with an introductory-level knowledge of signals and systems. Written by prominent, DSP pioneers, it provides thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete-time Fourier Analysis. By focusing on the general and universal concepts in discrete-time signal processing, it remains vital and relevant to the new challenges arising in the field -without limiting itself to specific technologies with relatively short life spans.

List of Examples

Preface

xix

Acknowledgements

xxv

Introduction

(7)

DISCRETE-TIME SIGNALS AND SYSTEMS

(86)

Introduction

(1)

Discrete-Time Signals: Sequences

(7)

Basic Sequences and Sequence Operations

(5)

Discrete-Time Systems

(6)

Memoryless Systems

(1)

Linear Systems

(2)

Time-Invariant Systems

(1)

Causality

(1)

Stability

(1)

Linear Time-Invariant Systems

(6)

Properties of Linear Time-Invariant Systems

(6)

Linear Constant-Coefficient Difference Equations

(6)

Frequency-Domain Representation of Discrete-Time Signals and Systems

(8)

Eigenfunctions for Linear Time-Invariant Systems

(6)

Suddenly Applied Complex Exponential Inputs

(2)

Representation of Sequences by Fourier Transforms

(7)

Symmetry Properties of the Fourier Transform

(3)

Fourier Transform Theorems

(7)

Linearity of the Fourier Transform

(1)

Time Shifting and Frequency Shifting

(1)

Time Reversal

(1)

Differentiation in Frequency

(1)

Parseval's Theorem

(1)

The Convolution Theorem

(1)

The Modulation or Windowing Theorem

(4)

Discrete-Time Random Signals

(5)

Summary

(1)

Problems

(24)

THE Z-TRANSFORM

(46)

Introduction

(1)

z-Transform

(11)

Properties of the Region of Convergence for the z-Transform

105

(6)

The Inverse z-Transform

111

(8)

Inspection Method

111

(1)

Partial Fraction Expansion

112

(4)

Power Series Expansion

116

(3)

z-Transform Properties

119

(7)

Linearity

119

(1)

Time Shifting

120

(1)

Multiplication by an Exponential Sequence

121

(1)

Differentiation of X (z)

122

(1)

Conjugation of a Complex Sequence

123

(1)

Time Reversal

123

(1)

Convolution of Sequences

124

(2)

Initial-Value Theorem

126

(1)

Summary of Some z-Transform Properties

126

(1)

Summary

126

(1)

Problems

127

(13)

SAMPLING OF CONTINUOUS-TIME SIGNALS

140

(100)

Introduction

140

(1)

Periodic Sampling

140

(2)

Frequency-Domain Representation of Sampling

142

(8)

Reconstruction of a Bandlimited Signal from Its Samples

150

(3)

Discrete-Time Processing of Continuous-Time Signals

153

(10)

Linear Time-Invariant Discrete-Time Systems

154

(6)

Impulse Invariance

160

(3)

Continuos-Time Processing of Discrete-Time Signals

163

(4)

Changing the Sampling Rate Using Discrete-Time Processing

167

(12)

Sampling Rate Reduction by an Integer Factor 167

167

(5)

Increasing the Sampling Rate by an Integer Factor

172

(4)

Changing the Sampling Rate by a Noninteger Factor

176

(3)

Multirate Signal Processing

179

(6)

Interchange of Filtering and Downsampling/Upsampling

179

(1)

Polyphase Decompositions

180

(2)

Polyphase Implementation of Decimation Filters

182

(1)

Polyphase Implementation of Interpolation Filters

183

(2)

Digital Processing of Analog Signals

185

(16)

Prefiltering to Avoid Aliasing

185

(2)

Analog-to-Digital (A/D) Conversion

187

(6)

Analysis of Quantization Errors

193

(4)

D/A Conversion

197

(4)

Oversampling and Noise Shaping in A/D and D/A Conversion

201

(12)

Oversampled A/D Conversion with Direct Quantization

201

(5)

Oversampled A/D Conversion with Noise Shaping

206

(4)

Oversampling and Noise Shaping in D/A Conversion

210

(3)

Summary

213

(1)

Problems

214

(26)

TRANSFORM ANALYSIS OF LINEAR TIME-INVARIANT SYSTEMS

240

(100)

Introduction

240

(1)

The Frequency Response of LTI Systems

241

(4)

Ideal Frequency-Selective Filters

241

(1)

Phase Distortion and Delay

242

(3)

System Functions for Systems Characterized by Linear Constant-Coefficient Difference Equations

245

(8)

Stability and Causality

247

(1)

Inverse Systems

248

(2)

Impulse Response for Rational System Functions

250

(3)

Frequency Response for Rational System Functions

253

(17)

Frequency Response of a Single Zero or Pole

258

(7)

Examples with Multiple Poles and Zeros

265

(5)

Relationship between Magnitude and Phase

270

(4)

All-Pass Systems

274

(6)

Minimum-Phase Systems

280

(11)

Minimum-Phase and All-Pass Decomposition

280

(2)

Frequency-Response Compensation

282

(5)

Properties of Minimum-Phase Systems

287

(4)

Linear Systems with Generalized Linear Phase

291

(20)

Systems with Linear Phase

292

(3)

Generalized Linear Phase

295

(2)

Causal Generalized Linear-Phase Systems

297

(11)

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

308

(3)

Summary

311

(1)

Problems

312

(28)

STRUCTURES FOR DISCRETE-TIME SYSTEMS

340

(99)

Introduction

340

(1)

Block Diagram Representation of Linear Constant-Coefficient Difference Equations

341

(7)

Signal Flow Graph Representation of Linear Constant-Coefficient Difference Equations

348

(6)

Basic Structures for IIR Systems

354

(9)

Direct Forms

354

(2)

Cascade Form

356

(3)

Parallel Form

359

(2)

Feedback in IIR Systems

361

(2)

Transposed Forms

363

(3)

Basic Network Structures for FIR systems

366

(4)

Direct Form

367

(1)

Cascade Form

367

(1)

Structures for Linear-Phase FIR Systems

368

(2)

Overview of Finite-Precision Numberical Effects

370

(7)

Number Representations

371

(3)

Quantization in Implementing Systems

374

(3)

The Effects of Coefficient Quantization

377

(14)

Effects of Coefficient quantization in FIR Systems

377

(2)

Example of Coefficient Quantization in an Elliptic Filter

379

(3)

Poles of Quantized Second-Order Sections

382

(2)

Effects of Coefficient Quantization if FIR Systems

384

(2)

Example of Quantization of an Optimum FIR Filter

386

(4)

Maintaining Linear Phase

390

(1)

Effects of Round-off Noise in Digital Filters

391

(22)

Analysis of Direct-Form IIR Structures

391

(8)

Scaling in Fixed-Point Implementations of IIR Systems

399

(4)

Example of Analysis of a Cascade IIR Structure

403

(7)

Analysis of Direct-Form FIR Systems

410

(2)

Floating-Point Realizations of Discrete-Time Systems

412

(1)

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

413

(5)

Limit Cycles dueto Round-off and Truncation

414

(2)

Limit Cycles Due to Overflow

416

(1)

Avoiding Limit Cycles

417

(1)

Summary

418

(1)

Problems

419

(20)

FILTER DESIGN TECHNIQUES

439

(102)

Introduction

439

(3)

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

442

(23)

Filter Design by Impulse Invariance

443

(7)

Bilinear Transformation

450

(4)

Examples of Bilinear Transformation Design

454

(11)

Design of FIR Filters by Windowing

465

(13)

Properties of Commonly Used Windows

467

(2)

Incorporation of Generalized Linear Phase

469

(5)

The Kaiser Window Filter Design Method

474

(4)

Relationship of the Kaiser Window to Other Windows

478

(1)

Examples of FIR Filter Design by the Kaiser Window Method

478

(8)

Highpass Filter

479

(3)

Discrete-Time Differentiators

482

(4)

Optimum Approximations of FIR Filters

486

(17)

Optimal Type I Lowpass Filters

491

(6)

Optimal Type II Lowpass Filters

497

(1)

The Parks-McClellan Algorithm

498

(3)

Characteristics of Optimum FIR Filters

501

(2)

Examples of FIR Equiripple Approximation

503

(7)

Lowpass Filter

503

(3)

Compensation for Zero-Order Hold

506

(1)

Bandpass Filter

507

(3)

Comments on IIR and FIR Discrete-Time Filters

510

(1)

Summary

511

(1)

Problems

511

(30)

The Discrete Fourier Transform

541

(88)

Introduction

541

(1)

Representation of Periodic Sequences: The Discrete Fourier Series

542

(4)

Properties of the Discrete Fourier Series

546

(5)

Linearity

546

(1)

Shift of a Sequence

546

(1)

Duality

547

(1)

Symmetry Properties

547

(1)

Periodic Convolution

548

(2)

Summary of Properties of the DFS Representation of Perodic Sequences

550

(1)

The Fourier Transform of Periodic Signals

551

(4)

Sampling the Fourier Transform

555

(4)

Fourier Representation of Finite-Duration Sequences: The Discrete Fourier Transform

559

(5)

Properties of the Discrete Fourier Transform

564

(12)

Linearity

564

(1)

Circular Shift of a Sequence

564

(3)

Duality

567

(1)

Symmetry Properties

568

(3)

Circular Convolution

571

(4)

Summary of Properties of the Discrete Fourier Transform

575

(1)

Linear Convolution Using the Discrete Fourier Transform

576

(13)

Linear Convolution of Two Finite-Length Sequences

577

(1)

Circular Convolution as Linear Convolution with Aliasing

577

(5)

Implementing Linear Time-Invariant Systems Using the DFT

582

(7)

The Discrete Consine Transform (DCT)

589

(10)

Definitions of the DCT

589

(1)

Definition of the DCT-1 and DCT-2

590

(3)

Relationship between the DFT and the DCT-1

593

(1)

Relationship between the DFT and the DCT-2

594

(1)

Energy Compaction Property of the DCT-2

595

(3)

Applications of the DCT

598

(1)

Summary

599

(30)

Problems

600

(29)

COMPUTATION OF THE DISCRETE FOURIER TRANSFORM

629

(64)

Introduction

629

(1)

Efficient Computation of the Discrete Fourier Transform

630

(3)

The Goertzel Algorithm

633

(2)

Decimation-in-Time FFT Algorithms

635

(11)

In-Place Computations

640

(3)

Alternative Forms

643

(3)

Decimation-inFrequency FFT Algiorithms

646

(6)

In-Place Computation

650

(1)

Alternative Forms

650

(2)

Practical Considerations

652

(3)

Indexing

652

(2)

Coefficients

654

(1)

Algorithms for More General Values of N

655

(1)

Implementation of the DFT Using Convolution

655

(6)

Overview of the Winograd Fourier Transform Algorithm

655

(1)

The Chirp Transform Algorithm

656

(5)

Effects of Finite Register Length

661

(8)

Summary

669

(1)

Problems

669

(24)

Fourier Analysis of Signals Using the Discrete Fourier Transform

693

(82)

Introduction

693

(1)

Fourier Analysis of Signals Using the DFT

694

(3)

DFT Analysis of Sinusoidal Signals

697

(17)

The Effect of Windowing

698

(5)

The Effect of Spectral Sampling

703

(11)

The Time-Dependent Fourier Transform

714

(8)

The Effect of the Window

717

(1)

Sampling in Time and Frequency

718

(4)

Block Convolution Using the Time-Dependent Fourier Transform

722

(1)

Fourier Analysis of Nonstationary Signals

723

(7)

Time-Dependent Fourier Analysis of Speech Signals

724

(4)

Time-Dependent Fourier Analysis of Radar Signals

728

(2)

Fourier Analysis of Stationary Random Signals: The Periodogram

730

(13)

The Periodogram

731

(2)

Properties of the Periodogram

733

(4)

Periodogram Averaging

737

(2)

Computation of Average Periodograms Using the DFT

739

(1)

An Example of Periodogram Analysis

739

(4)

Spectrum Analysis of Random Signals Using Estimates of the Autocorrelation Sequence

743

(11)

Computing Correlation and Power Spectrum Estimates Using the DFT

746

(2)

An Example of Power Spectrum Estimation Based on Estimation of the Autocorrelation Sequence

748

(6)

Summary

754

(1)

Problems

755

(20)

Discrete Hilbert Transforms

775

(36)

Introduction

775

(2)

Real- and Imaginary-Part Sufficiency of the Fourier Transform for Causal Sequences

777

(5)

Sufficiency Theorems for Finite-Length Sequences

782

(6)

Relationships Between Magnitude and Phase

788

(1)

Hilbert Transform Relations for Complex Sequences

789

(12)

Design of Hilbert Transformers

792

(4)

Representation of Bandpass Signals

796

(3)

Bandpass Sampling

799

(2)

Summary

801

(1)

Problems

802

(9)

Appendix A Random Signals

811

(1)

Discrete-Time Random Processes

811

(2)

Averages

813

(1)

Definitions

813

(2)

Time Averages

815

(2)

Properties of Correlation and Covariance Sequences

817

(1)

Fourier Transform Representation of Random Signals

818

(2)

Use of the z-Transform in Average Power Computations

820

(4)

Appendix B Continuous-Time Filters

824

(1)

Butterworth Lowpass Filters

824

(2)

Chebyshev Filters

826

(2)

Elliptic Filters

828

(2)

Appendix C Answers to Selected Basic Problems

830

(21)

Bibliography

851

(8)

Index

859

Amazon no longer offers textbook rentals. We do!

Discrete-Time Signal Processing

Discrete-Time Signal Processing

9780137549207

0137549202

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Discrete-Time Signal Processing

Discrete-Time Signal Processing

9780137549207

0137549202

Summary

Table of Contents

Supplemental Materials

Write a Review

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