Signals and Systems Continuous and Discrete

, by Ziemer, Rodger E.; Tranter, William H; Fannin, D. R.

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ISBN: 9780134964560 | 013496456X
Cover: Hardcover
Copyright: 2/10/1998

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A market leader in previous editions, this book continues to offer a complete survey of continuous and discrete linear systems.It utilizes a systems approach to solving practical engineering problems, rather than using the framework of traditional circuit theory. Numerous examples from circuit theory appear throughout, however, to illustrate the various systems techniques introduced. TheFourth Editionhas been thoroughly updated to effectively integrate the use of computers and to accurately reflect the latest theoretical advances.

1 Signal and System Modeling Concepts

(47)

1-1 Introduction

(1)

1-2 Examples of Systems

(6)

1-3 Signal Models

(20)

Examples of Deterministic Signals

(1)

Continuous-Time Versus Discrete-Time Signals

(2)

Periodic and Aperiodic Signals

(2)

Phasor Signals and Spectra

(5)

Singularity Functions

(11)

1-4 Energy and Power Signals

(2)

Average Power of a Periodic Signal

(1)

1-5 Energy and Power Spectral Densities

(2)

1-6 MATLAB in Signal Analysis

(3)

Summary

(2)

Further Reading

(1)

Problems

(9)

Computer Exercises

(2)

2 System Modeling and Analysis in the Time Domain

(53)

2-1 Introduction

(1)

2-2 System Modeling Concepts

(8)

Some Terminology

(1)

Representations for Systems

(4)

Properties of Systems

(3)

2-3 The Superposition Integral for Fixed, Linear Systems

(5)

2-4 Examples Illustrating Evaluation of the Convolution Integral

(6)

2-5 Impulse Response of a Fixed, Linear System

(3)

2-6 Superposition Integrals in Terms of Step Response

(4)

2-7 Frequency Response Function of a Fixed, Linear System

(3)

2-8 Stability of Linear Systems

(1)

2-9 System Modeling and Simulation

(9)

Summary

(3)

Further Reading

(1)

Problems

(8)

Computer Exercises

(2)

3 The Fourier Series

101

(49)

3-1 Introduction

101

(1)

3-2 Trigonometric Series

101

(2)

3-3 Obtaining Trigonometric Fourier Series Representations for Periodic Signals

103

(9)

3-4 The Complex Exponential Fourier Series

112

(7)

3-5 Symmetry Properties of the Fourier Series Coefficients

119

(1)

3-6 Parseval's Theorem

120

(4)

3-7 Line Spectra

124

(2)

3-8 Steady-State Response of a Fixed, Linear System to a Periodic Input: Distortionless Systems

126

(8)

*3-9 Rate of Convergence of Fourier Spectra

134

(2)

*3-10 Fourier Series and Signal Spaces

136

(4)

Summary

140

(2)

Further Reading

142

(1)

Problems

143

(6)

Computer Exercises

149

(1)

4 The Fourier Transform and Its Applications

150

(55)

4-1 Introduction

150

(1)

4-2 The Fourier Integral

150

(3)

4-3 Energy Spectral Density

153

(4)

4-4 Fourier Transforms in the Limit

157

(1)

4-5 Fourier Transform Theorems

157

(14)

4-6 System Analysis with the Fourier Transform

171

(4)

4-7 Steady-State System Response to Sinusoidal Inputs by Means of the Fourier Transform

175

(3)

4-8 Ideal Filters

178

(1)

4-9 Bandwith and Rise Time

178

(3)

*4-10 Window Functions and the Gibbs Phenomenon

181

(5)

*4-11 Fourier Transforms of Periodic Signals

186

(2)

*4-12 Applications of the Hilbert Transform

188

(1)

Analytic Signals

188

(1)

Causality

188

(1)

*4-13 The Discrete Fourier Transform

189

(4)

Summary

193

(1)

Further Reading

194

(1)

Problems

194

(10)

Computer Exercise

204

(1)

5 The Laplace Transform

205

(44)

5-1 Introduction

205

(1)

5-2 Examples of Evaluating Laplace Transforms

206

(3)

5-3 Some Laplace Transform Theorems

209

(11)

5-4 Inversion of Rational Functions

220

(12)

*5-5 The Inversion Integral and Its Use in Obtaining Inverse Laplace Transforms

232

(3)

*5-6 The Double-Sided Laplace Transform

235

(3)

Summary

238

(2)

Further Reading

240

(1)

Problems

240

(7)

Computer Exercises

247

(2)

6 Applications of the Laplace Transform

249

(63)

6-1 Introduction

249

(1)

6-2 Network Analysis Using the Laplace Transform

249

(13)

Laplace Transform Equivalent Circuit Elements

249

(4)

Mutual Inductance

253

(4)

Network Theorems in Terms of the Laplace Transform

257

(5)

6-3 Loop and Node Analyses of Circuits by Means of the Laplace Transform

262

(6)

Loop Analysis

262

(4)

Nodal Analysis

266

(2)

6-4 Transfer Functions

268

(6)

Definition of a Transfer Function

268

(1)

Properties of Transfer Function for Linear, Lumped Stable Systems

269

(1)

Components of System Response

270

(4)

Asymptotic and Marginal Stability

274

(1)

6-5 Stability and the Routh Array

274

(5)

6-6 Bode Plots

279

(8)

6-7 Block Diagrams

287

(7)

*6-8 Operational Amplifiers as Elements in Feedback Circuits

294

(2)

Summary

296

(2)

Further Reading

298

(1)

Problems

298

(13)

Computer Exercises

311

(1)

7 State-Variable Techniques

312

(38)

7-1 Introduction

312

(1)

7-2 State-Variable Concepts

312

(1)

7-3 Form of the State Equations

313

(3)

7-4 Time-Domain Solution of the State Equations

316

(3)

7-5 Frequency-Domain Solution of the State Equations

319

(2)

7-6 Finding the State Transition Matrix

321

(9)

7-7 State Equations for Electrical Networks

330

(4)

7-8 State Equations from Transfer Functions

334

(5)

*7-9 State Equations for Discrete-Time Systems

339

(4)

Summary

343

(1)

Further Reading

344

(1)

Problems

344

(5)

Computer Exercises

349

(1)

8 Discrete-Time Signals and Systems

350

(65)

8-1 Introduction

350

(1)

8-2 Analog-to-Digital Conversion

350

(17)

Sampling

351

(3)

Impulse-Train Sampling Model

354

(1)

Data Reconstruction

355

(8)

Quantizing and Encoding

363

(4)

8-3 The z-Transform

367

(15)

Definition of the z-Transform

367

(6)

Linearity

373

(1)

Initial Value and Final Value Theorems

374

(1)

Inverse z-Transform

375

(5)

Delay Operator

380

(2)

8-4 Difference Equations and Discrete-Time System

382

(13)

Properties of Systems

382

(6)

Difference Equations

388

(2)

Steady-State Frequency Response of a Linear Discrete-Time System

390

(3)

Frequency Response at f = 0 and f = 0.5fs

393

(2)

8-5 Example of a Discrete-Time System

395

(1)

*8-6 Inverse z-Transformation by the Inversion Integral

396

(2)

Summary

398

(3)

Further Reading

401

(1)

Problems

401

(11)

Computer Exercises

412

(3)

9 Analysis and Design of Digital Filters

415

(71)

9-1 Introduction

415

(1)

9-2 Structures of Digital Processors

415

(9)

Direct-Form Realizations

415

(1)

Cascade and Parallel Realizations

416

(8)

9-3 Discrete-Time Integration

424

(5)

Rectangular Integration

424

(1)

Trapezoidal Integration

425

(4)

9-4 Infinite Impulse Response (IIR) Filter Design

429

(19)

Synthesis in the Time Domain--Invariant Design

429

(9)

Design in the Frequency Domain--The Bilinear z-Transform

438

(7)

Bilinear z-Transform Bandpass Filters

445

(3)

9-5 Design of Finite-Duration Impulse Response (FIR) Digital Filters

448

(16)

FIR Filters--A General Design Technique

452

(1)

Causal Filters

453

(2)

Design Summary

455

(9)

9-6 Computer-Aided Design of Digital Filters

464

(5)

Summary

469

(2)

Further Reading

471

(1)

Problems

472

(11)

Computer Exercises

483

(3)

10 The Discrete Fourier Transform and Fast Fourier Transform Algorithms

486

(55)

10-1 Introduction

486

(1)

10-2 The DFT Compared with the Exponential Fourier Series: Error Sources in the DFT

486

(6)

10-3 Examples Illustrating the Computation of the DFT

492

(6)

10-4 Mathematical Derivation of the FFT

498

(7)

Decimation-in-Time FFT Algorithm

498

(3)

Decimation-in-Frequency FFT Algorithm

501

(4)

10-5 Properties of the DFT

505

(6)

10-6 Applications of the FFT

511

(10)

Filtering

511

(3)

Spectrum Analyzers

514

(1)

Convolution

514

(3)

Energy Spectral Density and Autocorrelation Functions

517

(3)

System Identification

520

(1)

Signal Restoration or Deconvolution

521

(1)

10-7 Windows and Their Properties

521

(5)

10-8 Selection of Parameters for Signal Processing with the DFT

526

(2)

*10-9 The Chirp-z-Transform Algorithm

528

(6)

Summary

534

(1)

Further Reading

535

(1)

Problems

535

(5)

Computer Exercises

540

(1)

Appendix A Comments and Hints on Using MATLAB

541

(5)

A-1 Introduction

541

(1)

A-2 Window and File Management

541

(1)

A-3 Getting Help

542

(3)

A-4 Programming Hints

545

(1)

References

545

(1)

Appendix B Systematic Procedures for Writing Governing Equations for Lumped Systems

546

(20)

B-1 Introduction

546

(1)

B-2 Lumped, Linear Components and Their Describing Equations

546

(5)

B-3 System Graphs

551

(6)

Node and Circuit Postulates

552

(3)

Topology of System Graphs

555

(2)

B-4 Choosing Independent Equations for a System

557

(4)

B-5 Writing State Equations for Lumped Linear Systems Using Graph Theory

561

(3)

Further Reading

564

(1)

Problems

564

(2)

Appendix C Functions of a Complex Variable--Summary of Important Definitions and Theorems

566

(8)

Further Reading

573

(1)

Appendix D Matrix Algebra

574

(4)

Appendix E Analog Filters

578

(27)

E-1 Group Delay and Phase Delay

578

(2)

E-2 Approximation of Ideal Filters by Practical Filters

580

(3)

Butterworth Filter

580

(1)

Bessel Filter

581

(1)

Chebyshev I Filter

581

(1)

Chebyshev II Filter

582

(1)

Elliptic Filter

582

(1)

E-3 Butterworth and Chebyshev Filters

583

(11)

Butterworth Filters

583

(2)

Chebyshev I Filter

585

(9)

E-4 Filter Transformations

594

(6)

Frequency Scaling

594

(2)

Low-Pass-to-Bandpass Transformation

596

(2)

Low-Pass-to-Band-Reject (Notch) Transformation

598

(2)

Further Reading

600

(1)

Problems

601

(2)

MATLAB Projects

603

(2)

Appendix F Mathematical Tables

605

(3)

Appendix G Index of MATLAB Functions

608

(4)

Appendix H Answers to Selected Problems

612

(7)

Index

619

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Signals and Systems Continuous and Discrete

Summary

Table of Contents

Supplemental Materials