Signal Processing First

, by McClellan, James H.; Schafer, Ronald W.; Yoder, Mark A.

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780130909992 | 0130909998
Cover: Hardcover
Copyright: 2/26/2003

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This best-selling, hands-on, multimedia package provides an introduction to fundamental concepts, specifically discrete-time systems, for beginning engineering students. Created and written by the same well-respected authors, it has been adopted in over 100 institutions worldwide since publication. This class-tested learning package is also widely used as a self-teaching tool to discover more about USP applications, multimedia signals, and MATLAB reg; . Unique features such as visual learning demonstrations, MATLAB laboratories, and a bank of solved homework problems are just a few of the things that make this an essential learning tool for mastering fundamental concepts in today's electrical and computer engineering curricula.

Preface

xiv

Introduction

(6)

Mathematical Representation of Signals

(2)

Mathematical Representation of Systems

(1)

Thinking About Systems

(1)

The Next Step

(1)

Sinusoids

(29)

Tuning Fork Experiment

(1)

Review of Sine and Cosine Functions

(2)

Sinusoidal Signals

(4)

Relation of Frequency to Period

(1)

Phase Shift and Time Shift

(2)

Sampling and Plotting Sinusoids

(2)

Complex Exponentials and Phasors

(5)

Review of Complex Numbers

(1)

Complex Exponential Signals

(1)

The Rotating Phasor Interpretation

(2)

Inverse Euler Formulas

(1)

Phasor Addition

(5)

Addition of Complex Numbers

(1)

Phasor Addition Rule

(1)

Phasor Addition Rule: Example

(1)

MATLAB Demo of Phasors

(1)

Summary of the Phasor Addition Rule

(1)

Physics of the Tuning Fork

(2)

Equations from Laws of Physics

(2)

General Solution to the Differential Equation

(1)

Listening to Tones

(1)

Time Signals: More Than Formulas

(1)

Summary and Links

(1)

Problems

(5)

Spectrum Representation

(35)

The Spectrum of a Sum of Sinusoids

(3)

Notation Change

(1)

Graphical Plot of the Spectrum

(1)

Beat Notes

(4)

Multiplication of Sinusoids

(1)

Beat Note Waveform

(1)

Amplitude Modulation

(2)

Periodic Waveforms

(4)

Synthetic Vowel

(1)

Example of a Nonperiodic Signal

(2)

Fourier Series

(3)

Fourier Series: Analysis

(1)

Fourier Series Derivation

(2)

Spectrum of the Fourier Series

(1)

Fourier Analysis of Periodic Signals

(6)

The Square Wave

(1)

DC Value of a Square Wave

(1)

Spectrum of a Square Wave

(1)

Synthesis of a Square Wave

(1)

Triangle Wave

(1)

Synthesis of a Triangle Wave

(1)

Convergence of Fourier Synthesis

(1)

Time--Frequency Spectrum

(3)

Stepped Frequency

(1)

Spectrogram Analysis

(1)

Frequency Modulation: Chirp Signals

(3)

Chirp or Linearly Swept Frequency

(2)

A Closer Look at Instantaneous Frequency

(1)

Summary and Links

(1)

Problems

(7)

Sampling and Aliasing

(30)

Sampling

(8)

Sampling Sinusoidal Signals

(2)

The Concept of Aliasing

(1)

Spectrum of a Discrete-Time Signal

(1)

The Sampling Theorem

(1)

Ideal Reconstruction

(1)

Spectrum View of Sampling and Reconstruction

(5)

Spectrum of a Discrete-Time Signal Obtained by Sampling

(1)

Over-Sampling

(2)

Aliasing Due to Under-Sampling

(1)

Folding Due to Under-Sampling

(1)

Maximum Reconstructed Frequency

(1)

Strobe Demonstration

(4)

Spectrum Interpretation

(1)

Discrete-to-Continuous Conversion

(5)

Interpolation with Pulses

(1)

Zero-Order Hold Interpolation

(1)

Linear Interpolation

(1)

Cubic Spline Interpolation

(1)

Over-Sampling Aids Interpolation

(1)

Ideal Bandlimited Interpolation

(1)

The Sampling Theorem

(1)

Summary and Links

(2)

Problems

(5)

FIR Filters

101

(29)

Discrete-Time Systems

102

(1)

The Running-Average Filter

102

(3)

The General FIR Filter

105

(6)

An Illustration of FIR Filtering

106

(1)

The Unit Impulse Response

107

(1)

Unit Impulse Sequence

107

(1)

Unit Impulse Response Sequence

108

(1)

The Unit-Delay System

109

(1)

Convolution and FIR Filters

110

(1)

Computing the Output of a Convolution

110

(1)

Convolution in MATLAB

111

(1)

Implementation of FIR Filters

111

(4)

Building Blocks

111

(1)

Multiplier

112

(1)

Adder

112

(1)

Unit Delay

112

(1)

Block Diagrams

113

(1)

Other Block Diagrams

113

(2)

Internal Hardware Details

115

(1)

Linear Time-Invariant (LTI) Systems

115

(3)

Time Invariance

116

(1)

Linearity

117

(1)

The FIR Case

117

(1)

Convolution and LTI Systems

118

(4)

Derivation of the Convolution Sum

118

(2)

Some Properties of LTI Systems

120

(1)

Convolution as an Operator

121

(1)

Commutative Property of Convolution

121

(1)

Associative Property of Convolution

121

(1)

Cascaded LTI Systems

122

(2)

Example of FIR Filtering

124

(2)

Summary and Links

126

(1)

Problems

126

(4)

Frequency Response of FIR Filters

130

(33)

Sinusoidal Response of FIR Systems

130

(2)

Superposition and the Frequency Response

132

(3)

Steady-State and Transient Response

135

(2)

Properties of the Frequency Response

137

(2)

Relation to Impulse Response and Difference Equation

137

(1)

Periodicity of H(ejw)

138

(1)

Conjugate Symmetry

138

(1)

Graphical Representation of the Frequency Response

139

(4)

Delay System

139

(1)

First-Difference System

140

(2)

A Simple Lowpass Filter

142

(1)

Cascaded LTI Systems

143

(2)

Running-Average Filtering

145

(6)

Plotting the Frequency Response

146

(2)

Cascade of Magnitude and Phase

148

(1)

Experiment: Smoothing an Image

149

(2)

Filtering Sampled Continuous-Time Signals

151

(4)

Example: Lowpass Averager

152

(2)

Interpretation of Delay

154

(1)

Summary and Links

155

(2)

Problems

157

(6)

z-Transforms

163

(33)

Definition of the z-Transform

164

(1)

The z-Transform and Linear Systems

165

(2)

The z-Transform of an FIR Filter

166

(1)

Properties of the z-Transform

167

(2)

The Superposition Property of the z-Transform

168

(1)

The Time-Delay Property of the z-Transform

168

(1)

A General z-Transform Formula

169

(1)

The z-Transform as an Operator

169

(2)

Unit-Delay Operator

169

(1)

Operator Notation

170

(1)

Operator Notation in Block Diagrams

170

(1)

Convolution and the z-Transform

171

(4)

Cascading Systems

173

(1)

Factoring z-Polynomials

174

(1)

Deconvolution

175

(1)

Relationship Between the z-Domain and the w-Domain

175

(6)

The z-Plane and the Unit Circle

176

(1)

The Zeros and Poles of H (z)

177

(1)

Significance of the Zeros of H (z)

178

(1)

Nulling Filters

179

(1)

Graphical Relation Between z and w

180

(1)

Useful Filters

181

(5)

The L-Point Running-Sum Filter

181

(2)

A Complex Bandpass Filter

183

(2)

A Bandpass Filter with Real Coefficients

185

(1)

Practical Bandpass Filter Design

186

(3)

Properties of Linear-Phase Filters

189

(1)

The Linear-Phase Condition

189

(1)

Locations of the Zeros of FIR Linear-Phase Systems

189

(1)

Summary and Links

190

(1)

Problems

191

(5)

IIR Filters

196

(49)

The General IIR Difference Equation

197

(1)

Time-Domain Response

198

(6)

Linearity and Time Invariance of IIR Filters

199

(1)

Impulse Response of a First-Order IIR System

200

(1)

Response to Finite-Length Inputs

201

(1)

Step Response of a First-Order Recursive System

202

(2)

System Function of an IIR Filter

204

(6)

The General First-Order Case

205

(1)

The System Function and Block-Diagram Structures

206

(1)

Direct Form I Structure

206

(1)

Direct Form II Structure

207

(1)

The Transposed Form Structure

208

(1)

Relation to the Impulse Response

209

(1)

Summary of the Method

209

(1)

Poles and Zeros

210

(2)

Poles or Zeros at the Origin or Infinity

211

(1)

Pole Locations and Stability

211

(1)

Frequency Response of an IIR Filter

212

(4)

Frequency Response using MATLAB

213

(1)

Three-Dimensional Plot of a System Function

214

(2)

Three Domains

216

(1)

The Inverse z-Transform and Some Applications

216

(4)

Revisiting the Step Response of a First-Order System

217

(1)

A General Procedure for Inverse z-Transformation

218

(2)

Steady-State Response and Stability

220

(3)

Second-Order Filters

223

(8)

z-Transform of Second-Order Filters

223

(1)

Structures for Second-Order IIR Systems

224

(1)

Poles and Zeros

225

(1)

Impulse Response of a Second-Order IIR System

226

(1)

Real Poles

227

(1)

Complex Poles

228

(3)

Frequency Response of Second-Order IIR Filter

231

(5)

Frequency Response via MATLAB

232

(1)

3-dB Bandwidth

232

(1)

Three-Dimensional Plot of System Functions

233

(3)

Example of an IIR Lowpass Filter

236

(1)

Summary and Links

237

(1)

Problems

238

(7)

Continuous-Time Signals and LTI Systems

245

(40)

Continuous-Time Signals

246

(2)

Two-Sided Infinite-Length Signals

246

(1)

One-Sided Signals

247

(1)

Finite-Length Signals

248

(1)

The Unit Impulse

248

(6)

Sampling Property of the Impulse

250

(2)

Mathematical Rigor

252

(1)

Engineering Reality

252

(1)

Derivative of the Unit Step

252

(2)

Continuous-Time Systems

254

(1)

Some Basic Continuous-Time Systems

254

(1)

Continuous-Time Outputs

255

(1)

Analogous Discrete-Time Systems

255

(1)

Linear Time-Invariant Systems

255

(5)

Time-Invariance

256

(1)

Linearity

256

(1)

The Convolution Integral

257

(2)

Properties of Convolution

259

(1)

Impulse Responses of Basic LTI Systems

260

(1)

Integrator

260

(1)

Differentiator

261

(1)

Ideal Delay

261

(1)

Convolution of Impulses

261

(2)

Evaluating Convolution Integrals

263

(7)

Delayed Unit-Step Input

263

(4)

Evaluation of Discrete Convolution

267

(1)

Square-Pulse Input

268

(1)

Very Narrow Square Pulse Input

269

(1)

Discussion of Convolution Examples

270

(1)

Properties of LTI Systems

270

(6)

Cascade and Parallel Combinations

270

(2)

Differentiation and Integration of Convolution

272

(1)

Stability and Causality

273

(3)

Using Convolution to Remove Multipath Distortion

276

(2)

Summary

278

(1)

Problems

279

(6)

Frequency Response

285

(22)

The Frequency Response Function for LTI Systems

285

(4)

Plotting the Frequency Response

287

(1)

Logarithmic Plot

288

(1)

Magnitude and Phase Changes

288

(1)

Response to Real Sinusoidal Signals

289

(6)

Cosine Inputs

290

(1)

Symmetry of H (jw)

290

(3)

Response to a General Sum of Sinusoids

293

(1)

Periodic Input Signals

294

(1)

Ideal Filters

295

(3)

Ideal Delay System

295

(1)

Ideal Lowpass Filter

296

(1)

Ideal Highpass Filter

297

(1)

Ideal Bandpass Filter

297

(1)

Application of Ideal Filters

298

(2)

Time-Domain or Frequency-Domain?

300

(1)

Summary/Future

301

(1)

Problems

302

(5)

Continuous-Time Fourier Transform

307

(39)

Definition of the Fourier Transform

308

(2)

Fourier Transform and the Spectrum

310

(2)

Limit of the Fourier Series

310

(2)

Existence and Convergence of the Fourier Transform

312

(1)

Examples of Fourier Transform Pairs

313

(9)

Right-Sided Real Exponential Signals

313

(1)

Bandwidth and Decay Rate

314

(1)

Rectangular Pulse Signals

314

(2)

Bandlimited Signals

316

(1)

Impulse in Time or Frequency

317

(1)

Sinusoids

318

(1)

Periodic Signals

319

(3)

Properties of Fourier Transform Pairs

322

(4)

The Scaling Property

322

(2)

Symmetry Properties of Fourier Transform Pairs

324

(2)

The Convolution Property

326

(6)

Frequency Response

326

(1)

Fourier Transform of a Convolution

327

(1)

Examples of the Use of the Convolution Property

328

(1)

Convolution of Two Bandlimited Functions

328

(1)

Product of Two Sinc Functions

329

(1)

Partial Fraction Expansions

330

(2)

Basic LTI Systems

332

(3)

Time Delay

332

(1)

Differentiation

333

(1)

Systems Described by Differential Equations

334

(1)

The Multiplication Property

335

(2)

The General Signal Multiplication Property

335

(1)

The Frequency Shifting Property

336

(1)

Table of Fourier Transform Properties and Pairs

337

(1)

Using the Fourier Transform for Multipath Analysis

337

(4)

Summary

341

(1)

Problems

342

(4)

Filtering, Modulation, and Sampling

346

(43)

Linear Time-Invariant Systems

346

(12)

Cascade and Parallel Configurations

347

(1)

Ideal Delay

348

(3)

Frequency Selective Filters

351

(1)

Ideal Lowpass Filter

351

(1)

Other Ideal Frequency Selective Filters

352

(1)

Example of Filtering in the Frequency-Domain

353

(2)

Compensation for the Effect of an LTI Filter

355

(3)

Sinewave Amplitude Modulation

358

(10)

Double-Sideband Amplitude Modulation

358

(4)

DSBAM with Transmitted Carrier (DSBAM-TC)

362

(4)

Frequency Division Multiplexing

366

(2)

Sampling and Reconstruction

368

(12)

The Sampling Theorem and Aliasing

368

(2)

Bandlimited Signal Reconstruction

370

(2)

Bandlimited Interpolation

372

(1)

Ideal C-to-D and D-to-C Converters

373

(2)

The Discrete-Time Fourier Transform

375

(1)

The Inverse DTFT

376

(1)

Discrete-Time Filtering of Continuous-Time Signals

377

(3)

Summary

380

(1)

Problems

381

(8)

Computing the Spectrum

389

(38)

Finite Fourier Sum

390

(1)

Too Many Fourier Transforms?

391

(2)

Relation of the DTFT to the CTFT

392

(1)

Relation of the DFT to the DTFT

393

(1)

Relation of the DFT to the CTFT

393

(1)

Time-Windowing

393

(2)

Analysis of a Sum of Sinusoids

395

(4)

DTFT of a Windowed Sinusoid

398

(1)

Discrete Fourier Transform

399

(6)

The Inverse DFT

400

(1)

Summary of the DFT Representation

401

(1)

The Fast Fourier Transform (FFT)

402

(1)

Negative Frequencies and the DFT

402

(1)

DFT Example

403

(2)

Spectrum Analysis of Finite-Length Signals

405

(2)

Spectrum Analysis of Periodic Signals

407

(1)

The Spectrogram

408

(12)

Spectrogram Display

409

(1)

Spectrograms in MATLAB

410

(1)

Spectrogram of a Sampled Periodic Signal

410

(1)

Resolution of the Spectrogram

411

(1)

Resolution Experiment

412

(1)

Spectrogram of a Musical Scale

413

(2)

Spectrogram of a Speech Signal

415

(3)

Filtered Speech

418

(2)

The Fast Fourier Transform (FFT)

420

(3)

Derivation of the FFT

420

(1)

FFT Operation Count

421

(2)

Summary and Links

423

(1)

Problems

424

(3)

A Complex Numbers

427

(16)

Introduction

428

(1)

Notation for Complex Numbers

428

(3)

Rectangular Form

428

(1)

Polar Form

429

(1)

Conversion: Rectangular and Polar

430

(1)

Difficulty in Second or Third Quadrant

431

(1)

Euler's Formula

431

(1)

Inverse Euler Formulas

432

(1)

Algebraic Rules for Complex Numbers

432

(2)

Complex Number Exercises

434

(1)

Geometric Views of Complex Operations

434

(4)

Geometric View of Addition

435

(1)

Geometric View of Subtraction

436

(1)

Geometric View of Multiplication

437

(1)

Geometric View of Division

437

(1)

Geometric View of the Inverse, z-1

437

(1)

Geometric View of the Conjugate, z*

438

(1)

Powers and Roots

438

(3)

Roots of Unity

439

(1)

Procedure for Finding Multiple Roots

440

(1)

Summary and Links

441

(1)

Problems

441

(2)

B Programming in MATLAB

443

(12)

MATLAB Help

444

(1)

Matrix Operations and Variables

444

(2)

The Colon Operator

445

(1)

Matrix and Array Operations

445

(1)

A Review of Matrix Multiplication

445

(1)

Pointwise Array Operations

446

(1)

Plots and Graphics

446

(1)

Figure Windows

447

(1)

Multiple Plots

447

(1)

Printing and Saving Graphics

447

(1)

Programming Constructs

447

(1)

MATLAB Built-in Functions

448

(1)

Program Flow

448

(1)

MATLAB Scripts

448

(1)

Writing a MATLAB Function

448

(3)

Creating A Clip Function

449

(2)

Debugging a MATLAB M-file

451

(1)

Programming Tips

451

(4)

Avoiding Loops

452

(1)

Repeating Rows or Columns

452

(1)

Vectorizing Logical Operations

452

(1)

Creating an Impulse

453

(1)

The Find Function

453

(1)

Seek to Vectorize

454

(1)

Programming Style

454

(1)

C Laboratory Projects

455

(23)

Introduction to MATLAB

457

(6)

Pre-Lab

457

(1)

Overview

457

(1)

Movies: MATLAB Tutorials

457

(1)

Getting Started

458

(1)

Warm-up

458

(1)

MATLAB Array Indexing

459

(1)

MATLAB Script Files

459

(1)

MATLAB Sound (optional)

460

(1)

Laboratory: Manipulating Sinusoids with MATLAB

460

(1)

Theoretical Calculations

461

(1)

Complex Amplitude

461

(1)

Lab Review Questions

461

(2)

Encoding and Decoding Touch-Tone Signals

463

(10)

Introduction

463

(1)

Review

463

(1)

Background: Telephone Touch-Tone Dialing

463

(1)

DTMF Decoding

464

(1)

Pre-Lab

464

(1)

Signal Concatenation

464

(1)

Comment on Efficiency

465

(1)

Encoding from a Table

465

(1)

Overlay Plotting

465

(1)

Warm-up: DTMF Synthesis

465

(1)

DTMF Dial Function

466

(1)

Simple Bandpass Filter Design

467

(1)

Lab: DTMF Decoding

468

(1)

Filter Bank Design: dtmfdesign.m

468

(1)

A Scoring Function: dtmfscore.m

469

(1)

DTMF Decode Function: dtmfrun.m

470

(1)

Testing

471

(1)

Telephone Numbers

471

(1)

Demo

472

(1)

Two Convolution GUIs

473

(5)

Introduction

473

(1)

Pre-Lab: Run the GUIs

473

(1)

Discrete-Time Convolution Demo

473

(1)

Continuous-Time Convolution Demo

474

(1)

Warm-up: Run the GUIs

475

(1)

Continuous-Time Convolution GUI

475

(1)

Discrete Convolution GUI

475

(1)

Lab Exercises

475

(1)

Continuous-Time Convolution

475

(1)

Continuous-Time Convolution Again

476

(1)

Discrete-Time Convolution

476

(2)

D CD-ROM Demos

478

(4)

Index

482

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Signal Processing First

Summary

Table of Contents

Supplemental Materials