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Digital Signal Processing Signals, Systems, and Filters

by: Antoniou, Andreas

Digital Signal Processing Signals, Systems, and Filters

by: Antoniou, Andreas

ISBN 13:
9780071454247
ISBN 10:
0071454241
Edition: 1st
Format: Hardcover
Copyright: 10/10/2005
Publisher: McGraw-Hill Education
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Summary

Digital Signal Processing is a rapidly growing academic discipline the world over. This new text utilizes MATLAB and the CD-based DSP Lab to provide readers with a fully interactive approach to mastering the fundamentals of DSP and filter design. DSP Lab allows readers to work problems without purchasing MATLAB

Preface

xix

Introduction to Digital Signal Processing

(28)

Introduction

(1)

Signals

(3)

Frequency-Domain Representation

(3)

Notation

(1)

Signal Processing

(7)

Analog Filters

(1)

Applications of Analog Filters

(3)

Digital Filters

(4)

Two DSP Applications

(6)

Processing of EKG signals

(1)

Processing of Stock-Exchange Data

(2)

References

(3)

The Fourier Series and Fourier Transform

(50)

Introduction

(1)

Fourier Series

(17)

Definition

(1)

Particular Forms

(4)

Theorems and Properties

(11)

Fourier Transform

(33)

Derivation

(3)

Particular Forms

(7)

Theorems and Properties

(16)

References

(1)

Problems

(6)

The z Transform

(52)

Introduction

(1)

Definition of z Transform

(1)

Convergence Properties

(2)

The z Transform as a Laurent Series

(2)

Inverse z Transform

(1)

Theorems and Properties

(9)

Elementary Discrete-Time Signals

(6)

z-Transform Inversion Techniques

101

(18)

Use of Binomial Series

103

(5)

Use of Convolution Theorem

108

(2)

Use of Long Division

110

(3)

Use of Initial-Value Theorem

113

(2)

Use of Partial Fractions

115

(4)

Spectral Representation of Discrete-Time Signals

119

(12)

Frequency Spectrum

119

(1)

Periodicity of Frequency Spectrum

120

(4)

Interrelations

124

(2)

References

126

(1)

Problems

126

(5)

Discrete-Time Systems

131

(70)

Introduction

131

(1)

Basic System Properties

132

(8)

Linearity

132

(2)

Time Invariance

134

(2)

Causality

136

(4)

Characterization of Discrete-Time Systems

140

(2)

Nonrecursive Systems

140

(1)

Recursive Systems

140

(2)

Discrete-Time System Networks

142

(13)

Network Analysis

143

(3)

Implementation of Discrete-Time Systems

146

(1)

Signal Flow-Graph Analysis

147

(8)

Introduction to Time-Domain Analysis

155

(8)

Convolution Summation

163

(8)

Graphical Interpretation

166

(3)

Alternative Classification

169

(2)

Stability

171

(3)

State-Space Representation

174

(27)

Computability

175

(1)

Characterization

176

(8)

Time-Domain Analysis

184

(2)

Applications of State-Space Method

186

(1)

References

186

(1)

Problems

186

(15)

The Application of the z Transform

201

(60)

Introduction

201

(1)

The Discrete-Time Transfer Function

202

(5)

Derivation of H(z) from Difference Equation

202

(2)

Derivation of H(z) from System Network

204

(1)

Derivation of H(z) from State-Space Characterization

205

(2)

Stability

207

(16)

Constraint on Poles

207

(4)

Constraint on Eigenvalues

211

(3)

Stability Criteria

214

(1)

Test for Common Factors

215

(1)

Schur-Cohn Stability Criterion

216

(1)

Schur-Cohn-Fujiwara Stability Criterion

217

(2)

Jury-Marden Stability Criterion

219

(3)

Lyapunov Stability Criterion

222

(1)

Time-Domain Analysis

223

(1)

Frequency-Domain Analysis

224

(21)

Steady-State Sinusoidal Response

224

(3)

Evaluation of Frequency Response

227

(1)

Periodicity of Frequency Response

228

(1)

Aliasing

229

(3)

Frequency Response of Digital Filters

232

(13)

Transfer Functions for Digital Filters

245

(6)

First-Order Transfer Functions

246

(1)

Second-Order Transfer Functions

246

(5)

Higher-Order Transfer Functions

251

(1)

Amplitude and Delay Distortion

251

(10)

References

254

(1)

Problems

254

(7)

The Sampling Process

261

(60)

Introduction

261

(2)

Fourier Transform Revisited

263

(15)

Impulse Functions

263

(9)

Periodic Signals

272

(2)

Unit-Step Function

274

(1)

Generalized Functions

274

(4)

Interrelation Between the Fourier Series and the Fourier Transform

278

(6)

Poisson's Summation Formula

284

(2)

Impulse-Modulated Signals

286

(8)

Interrelation Between the Fourier and z Transforms

288

(2)

Spectral Relationship Between Discrete- and Continuous-Time Signals

290

(4)

The Sampling Theorem

294

(2)

Aliasing

296

(1)

Graphical Representation of Interrelations

297

(1)

Processing of Continuous-Time Signals Using Digital Filters

298

(5)

Practical A/D and D/A Converters

303

(18)

References

311

(1)

Problems

311

(10)

The Discrete Fourier Transform

321

(68)

Introduction

321

(1)

Definition

322

(1)

Inverse DFT

322

(1)

Properties

323

(2)

Linearity

323

(1)

Periodicity

323

(1)

Symmetry

323

(2)

Interrelation Between the DFT and the z Transform

325

(8)

Frequency-Domain Sampling Theorem

328

(5)

Time-Domain Aliasing

333

(1)

Interrelation Between the DFT and the CFT

333

(2)

Time-Domain Aliasing

335

(1)

Interrelation Between the DFT and the Fourier Series

335

(2)

Window Technique

337

(21)

Continuous-Time Windows

337

(13)

Discrete-Time Windows

350

(2)

Periodic Discrete-Time Windows

352

(2)

Application of Window Technique

354

(4)

Simplified Notation

358

(1)

Periodic Convolutions

358

(4)

Time-Domain Periodic Convolution

359

(2)

Frequency-Domain Periodic Convolution

361

(1)

Fast Fourier-Transform Algorithms

362

(14)

Decimation-in-Time Algorithm

362

(8)

Decimation-in-Frequency Algorithm

370

(5)

Inverse DFT

375

(1)

Application of the FFT Approach to Signal Processing

376

(13)

Overlap-and-Add Method

377

(3)

Overlap-and-Save Method

380

(1)

References

381

(1)

Problems

382

(7)

Realization of Digital Filters

389

(36)

Introduction

389

(2)

Realization

391

(21)

Direct Realization

392

(3)

Direct Canonic Realization

395

(2)

State-Space Realization

397

(4)

Lattice Realization

401

(3)

Cascade Realization

404

(3)

Parallel Realization

407

(3)

Transposition

410

(2)

Implementation

412

(13)

Design Considerations

412

(1)

Systolic Implementations

412

(5)

References

417

(1)

Problems

417

(8)

Design of Nonrecursive (FIR) Filters

425

(38)

Introduction

425

(1)

Properties of Constant-Delay Nonrecursive Filters

426

(5)

Impulse Response Symmetries

426

(2)

Frequency Response

428

(2)

Location of Zeros

430

(1)

Design Using the Fourier Series

431

(3)

Use of Window Functions

434

(19)

Rectangular Window

435

(2)

von Hann and Hamming Windows

437

(2)

Blackman Window

439

(1)

Dolph-Chebyshev Window

440

(5)

Kaiser Window

445

(1)

Prescribed Filter Specifications

445

(8)

Other Windows

453

(1)

Design Based on Numerical-Analysis Formulas

453

(10)

References

458

(1)

Problems

459

(4)

Approximations for Analog Filters

463

(66)

Introduction

463

(2)

Basic Concepts

465

(10)

Characterization

465

(1)

Laplace Transform

465

(1)

The Transfer Function

466

(1)

Time-Domain Response

466

(3)

Frequency-Domain Analysis

469

(2)

Ideal and Practical Filters

471

(3)

Realizability Constraints

474

(1)

Butterworth Approximation

475

(6)

Derivation

475

(1)

Normalized Transfer Function

476

(3)

Minimum Filter Order

479

(2)

Chebyshev Approximation

481

(12)

Derivation

481

(4)

Zeros of Loss Function

485

(4)

Normalized Transfer Function

489

(1)

Minimum Filter Order

490

(3)

Inverse-Chebyshev Approximation

493

(4)

Normalized Transfer Function

493

(1)

Minimum Filter Order

494

(3)

Elliptic Approximation

497

(16)

Fifth-Order Approximation

497

(7)

Nth-Order Approximation (n Odd)

504

(1)

Zeros and Poles of L(--s2)

504

(3)

Nth-Order Approximation (n Even)

507

(1)

Specification Constraint

508

(1)

Normalized Transfer Function

509

(4)

Bessel-Thomson Approximation

513

(3)

Transformations

516

(13)

Lowpass-to-Lowpass Transformation

516

(1)

Lowpass-to-Bandpass Transformation

516

(3)

References

519

(1)

Problems

520

(9)

Design of Recursive (IIR) Filters

529

(34)

Introduction

529

(1)

Realizability Constraints

530

(1)

Invariant Impulse-Response Method

530

(4)

Modified Invariant Impulse-Response Method

534

(4)

Matched-z Transformation Method

538

(3)

Bilinear-Transformation Method

541

(8)

Derivation

541

(2)

Mapping Properties of Bilinear Transformation

543

(2)

The Warping Effect

545

(4)

Digital-Filter Transformations

549

(5)

General Transformation

549

(2)

Lowpass-to-Lowpass Transformation

551

(1)

Lowpass-to-Bandstop Transformation

552

(2)

Application

554

(1)

Comparison Between Recursive and Nonrecursive Designs

554

(9)

References

555

(1)

Problems

556

(7)

Recursive (IIR) Filters Satisfying Prescribed Specifications

563

(30)

Introduction

563

(1)

Design Procedure

564

(1)

Design Formulas

565

(12)

Lowpass and Highpass Filters

565

(3)

Bandpass and Bandstop Filters

568

(5)

Butterworth Filters

573

(2)

Chebyshev Filters

575

(1)

Inverse-Chebyshev Filters

576

(1)

Elliptic Filters

576

(1)

Design Using the Formulas and Tables

577

(9)

Constant Group Delay

586

(2)

Delay Equalization

586

(1)

Zero-Phase Filters

587

(1)

Amplitude Equalization

588

(5)

References

588

(1)

Problems

588

(5)

Random Signals

593

(24)

Introduction

593

(1)

Random Variables

593

(5)

Probability-Distribution Function

594

(1)

Probability-Density Function

594

(1)

Uniform Probability Density

594

(1)

Gaussian Probability Density

594

(1)

Joint Distributions

594

(1)

Mean Values and Moments

595

(3)

Random Processes

598

(1)

Notation

598

(1)

First-and Second-Order Statistics

599

(3)

Moments and Autocorrelation

602

(2)

Stationary Processes

604

(1)

Frequency-Domain Representation

604

(5)

Discrete-Time Random Processes

609

(1)

Filtering of Discrete-Time Random Signals

610

(7)

References

613

(1)

Problems

613

(4)

Effects of Finite Word Length in Digital Filters

617

(56)

Introduction

617

(1)

Number Representation

618

(9)

Binary System

618

(2)

Fixed-Point Arithmetic

620

(3)

Floating-Point Arithmetic

623

(2)

Number Quantization

625

(2)

Coefficient Quantization

627

(5)

Low-Sensitivity Structures

632

(6)

Case I

635

(1)

Case II

636

(2)

Product Quantization

638

(2)

Signal Scaling

640

(7)

Method A

640

(1)

Method B

641

(2)

Types of Scaling

643

(2)

Application of Scaling

645

(2)

Minimization of Output Roundoff Noise

647

(4)

Application of Error-Spectrum Shaping

651

(3)

Limit-Cycle Oscillations

654

(19)

Quantization Limit Cycles

654

(5)

Overflow Limit Cycles

659

(1)

Elimination of Quantization Limit Cycles

660

(5)

Elimination of Overflow Limit Cycles

665

(2)

References

667

(1)

Problems

668

(5)

Design of Nonrecursive Filters Using Optimization Methods

673

(46)

Introduction

673

(1)

Problem Formulation

674

(4)

Lowpass and Highpass Filters

675

(1)

Bandpass and Bandstop Filters

676

(1)

Alternation Theorem

677

(1)

Remez Exchange Algorithm

678

(5)

Initialization of Extremals

679

(1)

Location of Maxima of the Error Function

679

(2)

Computation of |E(ω)| and Pc(ω)

681

(1)

Rejection of Superfluous Potential Extremals

682

(1)

Computation of Impulse Response

683

(1)

Improved Search Methods

683

(8)

Selective Step-by-Step Search

683

(4)

Cubic Interpolation

687

(2)

Quadratic Interpolation

689

(1)

Improved Formulation

689

(2)

Efficient Remez Exchange Algorithm

691

(3)

Gradient Information

694

(6)

Property 1

695

(1)

Property 2

695

(1)

Property 3

695

(1)

Property 4

696

(1)

Property 5

696

(4)

Prescribed Specifications

700

(3)

Generalization

703

(4)

Antisymmetrical Impulse Response and Odd Filter Length

703

(2)

Even Filter Length

705

(2)

Digital Differentiators

707

(5)

Problem Formulation

707

(1)

First Derivative

708

(1)

Prescribed Specifications

708

(4)

Arbitrary Amplitude Responses

712

(1)

Multiband Filters

712

(7)

References

715

(1)

Additional References

716

(1)

Problems

716

(3)

Design of Recursive Filters Using Optimization Methods

719

(54)

Introduction

719

(1)

Problem Formulation

720

(2)

Newton's Method

722

(4)

Quasi-Newton Algorithms

726

(12)

Basic Quasi-Newton Algorithm

726

(3)

Updating Formulas for Matrix Sk+1

729

(1)

Inexact Line Searches

730

(4)

Practical Quasi-Newton Algorithm

734

(4)

Minimax Algorithms

738

(3)

Improved Minimax Algorithms

741

(4)

Design of Recursive Filters

745

(8)

Objective Function

745

(1)

Gradient Information

746

(1)

Stability

746

(1)

Minimum Filter Order

746

(1)

Use of Weighting

747

(6)

Design of Recursive Delay Equalizers

753

(20)

References

766

(1)

Additional References

766

(1)

Problems

767

(6)

Wave Digital Filters

773

(56)

Introduction

773

(1)

Sensitivity Considerations

774

(1)

Wave Network Characterization

775

(2)

Element Realizations

777

(14)

Impedances

778

(1)

Voltage Sources

779

(1)

Series Wire Interconnection

780

(2)

Parallel Wire Interconnection

782

(1)

2-Port Adaptors

783

(1)

Transformers

784

(2)

Unit Elements

786

(2)

Circulators

788

(1)

Resonant Circuits

788

(3)

Realizability Constraint

791

(1)

Lattice Wave Digital Filters

791

(7)

Analysis

791

(1)

Alternative Lattice Configuration

792

(4)

Digital Realization

796

(2)

Ladder Wave Digital Filters

798

(4)

Filters Satisfying Prescribed Specifications

802

(3)

Frequency-Domain Analysis

805

(2)

Scaling

807

(1)

Elimination of Limit-Cycle Oscillations

808

(2)

Related Synthesis Methods

810

(1)

A Cascade Synthesis Based on the Wave Characterization

811

(8)

Generalized-Immittance Converters

811

(1)

Analog G-CGIC Configuration

811

(1)

Digital G-CGIC Configuration

812

(2)

Cascade Synthesis

814

(3)

Signal Scaling

817

(1)

Output Noise

818

(1)

Choice of Structure

819

(10)

References

820

(2)

Problems

822

(7)

Digital Signal Processing Applications

829

(62)

Introduction

829

(1)

Sampling-Frequency Conversion

830

(9)

Decimators

830

(3)

Interpolators

833

(6)

Sampling Frequency Conversion by a Noninteger Factor

839

(1)

Design Considerations

839

(1)

Quadrature-Mirror-Image Filter Banks

839

(12)

Operation

840

(4)

Elimination of Aliasing Errors

844

(2)

Design Considerations

846

(3)

Perfect Reconstruction

849

(2)

Hilbert Transformers

851

(11)

Design of Hilbert Transformers

854

(5)

Single-Sideband Modulation

859

(2)

Sampling of Bandpassed Signals

861

(1)

Adaptive Digital Filters

862

(12)

Wiener Filters

865

(2)

Newton Algorithm

867

(1)

Steepest-Descent Algorithm

867

(3)

Least-Mean-Square Algorithm

870

(1)

Recursive Filters

871

(1)

Applications

872

(2)

Two-Dimensional Digital Filters

874

(17)

Two-Dimensional Convolution

875

(1)

Two-Dimensional z Transform

875

(1)

Two-Dimensional Transfer Function

875

(1)

Stability

876

(1)

Frequency-Domain Analysis

877

(3)

Types of 2-D Filters

880

(1)

Approximations

881

(1)

Applications

881

(1)

References

882

(2)

Additional References

884

(1)

Problems

884

(7)

Appendix A. Complex Analysis

891

(34)

A.1 Introduction

891

(1)

A.2 Complex Numbers

892

(7)

A.2.1 Complex Arithmetic

894

(1)

A.2.2 De Moivre's Theorem

894

(1)

A.2.3 Euler's Formula

895

(1)

A.2.4 Exponential Form

896

(1)

A.2.5 Vector Representation

897

(1)

A.2.6 Spherical Representation

898

(1)

A.3 Functions of a Complex Variable

899

(7)

A.3.1 Polynomials

899

(1)

A.3.2 Inverse Algebraic Functions

900

(1)

A.3.3 Trigonometric Functions and Their Inverses

900

(1)

A.3.4 Hyperbolic Functions and Their Inverses

901

(1)

A.3.5 Multi-Valued Functions

902

(2)

A.3.6 Periodic Functions

904

(1)

A.3.7 Rational Algebraic Functions

905

(1)

A.4 Basic Principles of Complex Analysis

906

(5)

A.4.1 Limit

906

(1)

A.4.2 Differentiability

907

(1)

A.4.3 Analyticity

907

(1)

A.4.4 Zeros

908

(1)

A.4.5 Singularities

908

(2)

A.4.6 Zero-Pole Plots

910

(1)

A.5 Series

911

(4)

A.6 Laurent Theorem

915

(4)

A.7 Residue Theorem

919

(1)

A.8 Analytic Continuation

920

(1)

A.9 Conformal Transformations

921

(4)

References

924

(1)

Appendix B. Elliptic Functions

925

(14)

B.1 Introduction

925

(1)

B.2 Elliptic Integral of the First Kind

925

(2)

B.3 Elliptic Functions

927

(3)

B.4 Imaginary Argument

930

(2)

B.5 Formulas

932

(1)

B.6 Periodicity

932

(2)

B.7 Transformation

934

(2)

B.8 Series Representation

936

(3)

References

937

(2)

Index

939

Amazon no longer offers textbook rentals. We do!

Digital Signal Processing Signals, Systems, and Filters

Digital Signal Processing Signals, Systems, and Filters

9780071454247

0071454241

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Digital Signal Processing Signals, Systems, and Filters

Digital Signal Processing Signals, Systems, and Filters

9780071454247

0071454241

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

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