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Linear Systems and Signals

by: Lathi, B. P.

Linear Systems and Signals

by: Lathi, B. P.

ISBN 13:
9780195151299
ISBN 10:
0195151291
Format: Hardcover
Copyright: 10/04/2001
Publisher: Oxford University Press
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Summary

This introductory level book gives comprehensive treatment to signals andlinear systems. It emphasizes the physical appreciation of concepts rather thanthe mere mathematical manipulation of symbols. Mathematics is used to enhancephysical and intuitive understanding, instead of to prove axiomatic theory. Thisconveniently organized book is divided into five parts and allows for theflexible teaching of discrete-time and continuous-time systems. Whereverpossible, theoretical results are interpreted heuristically and are supported bycarefully chosen examples and analogies.

Preface

PART I: INTRODUCTION

B. Background

(646)

Complex Numbers

(13)

A Historical Note

(3)

Algebra of Complex Numbers

(10)

Sinusoids

(9)

Addition of Sinusoids

(3)

Sinusoids in Terms of Exponentials: Euler's Formula

(1)

Generalized Sinusoids: Complex Frequency

(2)

Sketching Signals

(4)

Monotonic Exponentials

(1)

Exponentially Varying Sinusoid

(2)

Amplitude Modulated Sinusoid

(1)

Some Useful Signal Operations

(5)

Time-Shifting

(1)

Time-Scaling

(2)

Time-Inversion

(1)

Combined Operations

(1)

Mathematical Description of a Signal from Its Sketch

(3)

Even and Odd Functions

(2)

Some Properties of Even and Odd Functions

(1)

Even and Odd Components of a Signal

(1)

Cramer's Rule

(2)

Partial fraction expansion

(10)

Method of Clearing Fractions

(1)

Heaviside ``Cover-up'' Method

(5)

Mixture of Clearing Fractions and Heaviside ``Cover-up''

(2)

Partial Fraction Expansion of Improper F(x) with m = n

(1)

Modified Partial Fractions

(1)

Vectors and Matrices

(13)

Some Definitions and Properties

(1)

Matrix Algebra

(5)

Derivatives and Integrals of a Matrix

(1)

Characteristic Equation of a Matrix: Cayley-Hamilton Theorem

(2)

Computation of an Exponential and a Power of a Matrix

(2)

Miscellaneous

(5)

L'Hopital's Rule

(1)

Taylor and Maclaurin Series

(1)

Power Series Expansion

(1)

Sums

(1)

Complex Numbers

(1)

Trigonometric Identities

(1)

Indefinite Integrals

(1)

Differentiation Table

(1)

Some Useful Constants

(1)

Solution of Quadratic and Cubic Equations

(2)

Introduction to Systems

(36)

Signals and Systems

(3)

Classification of Systems

(10)

Linear and Nonlinear Systems

(4)

Time-Invariant and Time-varying Parameter Systems

(1)

Instantaneous and Dynamic Systems

(1)

Causal and Noncausal Systems

(3)

Lumped-Parameter and Distributed Parameter Systems

(1)

Continuous-Time and Discrete-Time Systems

(1)

Analog and Digital Systems

(1)

System Model: Input-output Description

(8)

Electrical Systems

(2)

Mechanical Systems

(4)

Electromechanical Systems

(1)

Simultaneous Differential Equations

(2)

Internal and External Description of a System

(4)

Large Systems

(1)

State-Space Description of a System

(2)

Summary

(7)

PART II: TIME-DOMAIN ANALYSIS OF LTI SYSTEMS

Time-Domain Analysis: Continuous-Time Systems

105

(84)

Introduction

105

(2)

System Response to Internal Conditions: Zero-Input response

107

(13)

Some Insights Into the Zero-Input Behavior of a System

118

(2)

Unit Impulse Function

120

(7)

The Unit Impulse response h(t)

123

(4)

System Response to External Input: Zero-State Response

127

(23)

The Convolution Integral

130

(8)

Graphical Understanding of Convolution

138

(11)

Why Convolution? An Intuitive Explanation of System response

149

(1)

Some Reflections on the Use of Impulse Function

150

(1)

Numerical Convolution

150

(6)

System Stability

156

(5)

System Response to Bounded Inputs

159

(2)

Intuitive Insights In System Behavior

161

(9)

Dependence of System Behavior on Characteristic Modes

161

(2)

Response-Time of a System: The System Time-Constant

163

(1)

Time-Constant and Rise-Time of a System

164

(1)

Time-Constant and Filtering

165

(1)

Time-Constant and Pulse Dispersion (Spreading)

166

(1)

Time-Constant and Rate of Information transmission

167

(1)

Resonance Phenomenon

167

(3)

Classical Solution of Differential equations

170

(7)

Forced response: Method of Undetermined Coefficients

170

(7)

Determining The Impulse Response

177

(2)

Summary

179

(10)

Time-Domain Analysis: Discrete-Time Systems

189

(60)

Discrete-Time Systems

189

(6)

Discrete-Time System Equations

195

(5)

Initial Conditions and Interative solution of Difference Equations

196

(4)

System Response to Internal Conditions: Zero-Input Response

200

(8)

Unit Impulse Response h[k]

208

(5)

Determining Impulse Response h[k]

209

(4)

System Response to External Input: Zero-State Response

213

(10)

Graphical Procedure for Convolution Sum

220

(3)

System Stability

223

(7)

System Response to Bounded Inputs

229

(1)

Intuitive insights In System Behavior

230

(1)

Classical Solution of Linear Difference Equations

230

(5)

Determining Impulse Response

235

(2)

Summary

237

(12)

PART III: FREQUENCY-DOMAIN (TRANSFORM) ANALYSIS OF LTI SYSTEMS

Continuous-Time Systems: Laplace Transform Analysis

249

(104)

The Laplace Transform

249

(16)

Finding Inverse Transform

255

(10)

Some Properties of the Laplace Transform

265

(9)

Transform Solution of Differential and Integro-Differential Equations

274

(11)

The Zero-State Response of LTIC Systems: The Transfer Function

278

(3)

Relationship Between h(t) and H(s)

281

(1)

Frequency-Domain Interpretation of the Transfer function

282

(2)

Physical Interpretation of the Laplace Transform

284

(1)

Analysis of Electrical Networks: Transformed Network Method

285

(13)

Analysis of Active Circuits

294

(3)

Initial and Final Values

297

(1)

Block Diagrams

298

(5)

System Realization

303

(12)

Canonical or Direct-Form Realization

304

(5)

Cascade and Parallel Realizations

309

(3)

System Realization Using Operational Amplifiers

312

(3)

Frequency-Response of an LTIC System

315

(14)

Dependence of Frequency Response on Poles and Zeros of H(s)

322

(7)

Bilateral Laplace Transform

329

(8)

Linear System Analysis Using Bilateral Transform

335

(2)

Second Canonical Realization

337

(2)

Summary

339

(14)

Discrete-Time Systems: Z-Transform Analysis

353

(62)

The Z-Transform

353

(10)

Finding the Inverse Transform

357

(6)

Some Properties of the Z-Transform

363

(5)

Z-Transform solution of Difference equations

368

(9)

Zero-State Response of LTID Systems: The Transfer Function

372

(3)

Relationship Between h[k] and H[z]

375

(1)

Frequency-Domain Interpretation of the Transfer Function

376

(1)

Physical Interpretation of the Z-Transform

376

(1)

System Realization

377

(3)

Frequency Response of Discrete-Time Systems

380

(16)

Periodic Nature of Frequency Response

385

(1)

Aliasing and Sampling Rate

386

(2)

Dependence of Frequency Response on Poles and Zeros of H[z]

388

(8)

Connection Between the Z-Transform and Laplace Transform

396

(3)

Bilateral Z-Transform

399

(5)

Analysis of LTID Systems Using Bilateral Z-Transform

402

(2)

Summary

404

(11)

PART IV: SIGNAL ANALYSIS

Continuous-Time Signal Analysis: The Fourier Series

415

(59)

Representation of Periodic Signals by Trigonometric Fourier Series

415

(23)

The Fourier Spectrum

421

(8)

Effect of Symmetry

429

(2)

Determining the Fundamental Frequency and Period

431

(1)

Role of Amplitude and Phase Spectra in Wave Shaping

432

(6)

Exponential Fourier Series

438

(11)

Exponential Fourier Spectra

442

(6)

Why Use exponentials?

448

(1)

Iternate View of Fourier Representation: Signal-Vector Analogy

449

(18)

Vector Comparison

449

(2)

Signal Comparison

451

(2)

Orthogonal Vector Space

453

(2)

Orthogonal Signal Space

455

(6)

Gibbs Phenomenon

461

(3)

Some Examples of Orthogonal functions

464

(3)

Summary

467

(7)

Continuous-Time Signal Analysis: The Fourier Transform

474

(58)

Nonperiodic Signal Representation By Fourier Integral

474

(6)

Physical Appreciation of the Fourier Transform

480

(4)

Connection Between the Fourier and Laplace Transforms

482

(2)

Transform of Some Useful Functions

484

(6)

Some Properties of the Fourier Transform

490

(16)

Symmetry of the Direct and Inverse Transform Operation: Time-Frequency Duality

492

(1)

Duality Property

493

(1)

Scaling Property

494

(2)

Time-Shifting Property

496

(2)

Frequency-shifting Property

498

(4)

Convolution

502

(1)

Time-Differentiation and Integration

503

(3)

LTI System Analysis by Fourier Transform

506

(2)

Signal Distortion During Transmission

508

(3)

Ideal and Practical Filters

511

(3)

Thinking in Time-Domain and Frequency-Domain: Two-Dimentional View of Signals and Systems

514

(1)

Signal Energy

515

(3)

Data Truncation: Window Functions

518

(4)

Summary

522

(10)

Sampling

532

(33)

The Sampling Theorem

532

(10)

Practical Difficulties in Signal Reconstruction

534

(4)

Some Applications of the Sampling Theorem

538

(4)

Dual of the Sampling Theorem: Spectral Sampling

542

(1)

Numerical Computation of Fourier Transform: The Discrete Fourier Transform (DFT)

543

(16)

Some Properties of DFT

552

(5)

Fast Fourier Transform (FFT)

557

(2)

Summary

559

(6)

Analysis of Discrate-Time Signals

565

(30)

Discrete-Time Periodic Signals

565

(9)

Representation of Periodic Signals: Discrete-Time Fourier Series

566

(8)

Nonperiodic Signals: The Discrete-Time Fourier Transform (DTFT)

574

(8)

Relationship of the DTFT to Z-transform

581

(1)

Properties of DTFT

582

(1)

LTID System analysis by DTFT

583

(2)

Relationships Among Various Transforms

585

(3)

Derivation of the Z-Transform Pair

588

(1)

Summary

589

(6)

PART V: STATE-SPACE ANALYSIS

State-Space Analysis

595

(54)

Introduction

595

(3)

Systematic Procedure for Determining State Equations

598

(12)

Electrical Circuits

599

(2)

State Equations From Transfer Function

601

(9)

Solution of State Equations

610

(12)

Laplace Transform Solution of State Equations

610

(5)

Time-Domain solution of State Equations

615

(7)

Linear Transformation of State Vector

622

(8)

Diagonalization of Matrix A

626

(4)

Controllability and Observability

630

(6)

Inadequacy of transfer function Description

635

(1)

State-Space Analysis of Discrete-Time Systems

636

(6)

Solution in State-Space

638

(3)

Z-Transform Solution

641

(1)

Summary

642

(7)

Supplementary Reading

649

(2)

Index

651

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Linear Systems and Signals

Linear Systems and Signals

9780195151299

0195151291

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Linear Systems and Signals

Linear Systems and Signals

9780195151299

0195151291

Summary

Table of Contents

Supplemental Materials

Write a Review

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