A practical and accessible guide to understanding digital signal processing Introduction to Digital Signal Processing and Filter Design was developed and fine-tuned from the author's twenty-five years of experience teaching classes in digital signal processing. Following a step-by-step approach, students and professionals quickly master the fundamental concepts and applications of discrete-time signals and systems as well as the synthesis of these systems to meet specifications in the time and frequency domains. Striking the right balance between mathematical derivations and theory, the book features: * Discrete-time signals and systems * Linear difference equations * Solutions by recursive algorithms * Convolution * Time and frequency domain analysis * Discrete Fourier series * Design of FIR and IIR filters * Practical methods for hardware implementation A unique feature of this book is a complete chapter on the use of a MATLAB(r) tool, known as the FDA (Filter Design and Analysis) tool, to investigate the effect of finite word length and different formats of quantization, different realization structures, and different methods for filter design. This chapter contains material of practical importance that is not found in many books used in academic courses. It introduces students in digital signal processing to what they need to know to design digital systems using DSP chips currently available from industry. With its unique, classroom-tested approach, Introduction to Digital Signal Processing and Filter Design is the ideal text for students in electrical and electronic engineering, computer science, and applied mathematics, and an accessible introduction or refresher for engineers and scientists in the field. An Instructor's Manual presenting detailed solutions to all the problems in the book is available online from the Wiley editorial department. An Instructor Support FTP site is also available.

B. A. SHENOI, PHD, is Professor, Department of Electrical Engineering, Wright State University. Dr. Shenoi is internationally recognized for his research in active and digital filter theory and has published more than fifty papers on that topic in professional journals. He is a Life Fellow of the IEEE, a recipient of the Golden Jubilee Medal from the IEEE Circuits and Systems Society, and a recipient of the IEEE's Third Millennium Gold Medal.

Preface

xi

Introduction

1

(31)

Introduction

1

(1)

Applications of DSP

1

(2)

Discrete-Time Signals

3

(16)

Modeling and Properties of Discrete-Time Signals

8

(1)

Unit Pulse Function

9

(1)

Constant Sequence

10

(1)

Unit Step Function

10

(2)

Real Exponential Function

12

(1)

Complex Exponential Function

12

(2)

Properties of cos(ω0n)

14

(5)

History of Filter Design

19

(4)

Analog and Digital Signal Processing

23

(5)

Operation of a Mobile Phone Network

25

(3)

Summary

28

(4)

Problems

29

(1)

References

30

(2)

Time-Domain Analysis and z Transform

32

(80)

A Linear, Time-Invariant System

32

(9)

Models of the Discrete-Time System

33

(3)

Recursive Algorithm

36

(2)

Convolution Sum

38

(3)

z Transform Theory

41

(10)

Definition

41

(8)

Zero Input and Zero State Response

49

(1)

Linearity of the System

50

(1)

Time-Invariant System

50

(1)

Using z Transform to Solve Difference Equations

51

(8)

More Applications of z Transform

56

(2)

Natural Response and Forced Response

58

(1)

Solving Difference Equations Using the Classical Method

59

(5)

Transient Response and Steady-State Response

63

(1)

z Transform Method Revisited

64

(1)

Convolution Revisited

65

(5)

A Model from Other Models

70

(7)

Review of Model Generation

72

(5)

Stability

77

(4)

Jury--Marden Test

78

(3)

Solution Using MATLAB Functions

81

(12)

Summary

93

(19)

Problems

94

(16)

References

110

(2)

Frequency-Domain Analysis

112

(74)

Introduction

112

(1)

Theory of Sampling

113

(9)

Sampling of Bandpass Signals

120

(2)

DTFT and IDTFT

122

(16)

Time-Domain Analysis of Noncausal Inputs

125

(2)

Time-Shifting Property

127

(1)

Frequency-Shifting Property

127

(1)

Time Reversal Property

128

(10)

DTFT of Unit Step Sequence

138

(9)

Differentiation Property

139

(3)

Multiplication Property

142

(3)

Conjugation Property

145

(1)

Symmetry Property

145

(2)

Use of MATLAB to Compute DTFT

147

(7)

DTFS and DFT

154

(16)

Introduction

154

(2)

Discrete-Time Fourier Series

156

(3)

Discrete Fourier Transform

159

(1)

Reconstruction of DTFT from DFT

160

(1)

Properties of DTFS and DFT

161

(9)

Fast Fourier Transform

170

(2)

Use of MATLAB to Compute DFT and IDFT

172

(5)

Summary

177

(9)

Problems

178

(7)

References

185

(1)

Infinite Impulse Response Filters

186

(63)

Introduction

186

(3)

Magnitude Approximation of Analog Filters

189

(23)

Maximally Flat and Butterworth Approximation

191

(3)

Design Theory of Butterworth Lowpass Filters

194

(8)

Chebyshev I Approximation

202

(1)

Properties of Chebyshev Polynomials

202

(2)

Design Theory of Chebyshev I Lowpass Filters

204

(4)

Chebyshev II Approximation

208

(2)

Design of Chebyshev II Lowpass Filters

210

(2)

Elliptic Function Approximation

212

(1)

Analog Frequency Transformations

212

(7)

Highpass Filter

212

(1)

Bandpass Filter

213

(3)

Bandstop Filter

216

(3)

Digital Filters

219

(1)

Impulse-Invariant Transformation

219

(2)

Bilinear Transformation

221

(5)

Digital Spectral Transformation

226

(4)

Allpass Filters

230

(1)

IIR Filter Design Using MATLAB

231

(7)

Yule--Walker Approximation

238

(2)

Summary

240

(9)

Problems

240

(7)

References

247

(2)

Finite Impulse Response Filters

249

(54)

Introduction

249

(2)

Notations

250

(1)

Linear Phase Fir Filters

251

(10)

Properties of Linear Phase FIR Filters

256

(5)

Fourier Series Method Modified by Windows

261

(12)

Gibbs Phenomenon

263

(3)

Use of Window Functions

266

(2)

FIR Filter Design Procedures

268

(5)

Design of Windowed FIR Filters Using MATLAB

273

(7)

Estimation of Filter Order

273

(2)

Design of the FIR Filter

275

(5)

Equiripple Linear Phase FIR Filters

280

(5)

Design of Equiripple FIR Filters Using MATLAB

285

(4)

Use of MATLAB Program to Design Equiripple FIR Filters

285

(4)

Frequency Sampling Method

289

(3)

Summary

292

(11)

Problems

294

(7)

References

301

(2)

Filter Realizations

303

(51)

Introduction

303

(2)

FIR Filter Realizations

305

(7)

Lattice Structure for FIR Filters

309

(1)

Linear Phase FIR Filter Realizations

310

(2)

IIR Filter Realizations

312

(8)

Allpass Filters in Parallel

320

(7)

Design Procedure

325

(1)

Lattice--Ladder Realization

326

(1)

Realization of FIR and IIR Filters Using MATLAB

327

(19)

MATLAB Program Used to Find Allpass Filters in Parallel

334

(12)

Summary

346

(8)

Problems

347

(6)

References

353

(1)

Quantized Filter Analysis

354

(27)

Introduction

354

(1)

Filter Design-Analysis Tool

355

(5)

Quantized Filter Analysis

360

(1)

Binary Numbers and Arithmetic

360

(7)

Quantization Analysis of IIR Filters

367

(8)

Quantization Analysis of FIR Filters

375

(4)

Summary

379

(2)

Problems

379

(1)

References

379

(2)

Hardware Design Using DSP Chips

381

(10)

Introduction

381

(1)

Simulink and Real-Time Workshop

381

(2)

Design Preliminaries

383

(2)

Code Generation

385

(1)

Code Composer Studio

386

(2)

Simulator and Emulator

388

(1)

Embedded Target with Real-Time Workshop

389

(1)

Conclusion

389

(2)

References

390

(1)

MATLAB Primer

391

(24)

Introduction

391

(14)

Vectors, Arrays, and Matrices

392

(1)

Matrix Operations

393

(5)

Scalar Operations

398

(2)

Drawing Plots

400

(1)

MATLAB Functions

400

(1)

Numerical Format

401

(1)

Control Flow

402

(1)

Edit Window and M-file

403

(2)

Signal Processing Toolbox

405

(10)

List of Functions in Signal Processing Toolbox

406

(8)

References

414

(1)

Index

415

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