Signals and Systems

by Chen, Chi-Tsong

Edition: 3rd

ISBN13: 9780195156614

ISBN10: 0195156617

Format: Hardcover

Pub. Date: 2004-03-18

Publisher(s): Oxford University Press

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Summary

The third edition of Signals and Systems prepares students for real-world engineering applications. It is concise, focused, and practical. The text introduces basic concepts in signals and systems and their associated mathematical and computational tools. It also stresses the most importantconcepts in signal analysis (frequency spectra) and system analysis (stability and frequency responses) and uses them throughout, including the study of seismometers and accelerometers.Signals and Systems, 3/e, introduces every term carefully and develops every topic logically. It distinguishes amplitudes and magnitudes, as well as lumped and distributed systems. It presents engineering concepts as early as possible and discusses transform theory only as needed. Also, the textemploys transfer functions and state-space equations only in the contexts where they are most efficient. Transfer functions are used exclusively in qualitative analysis and design, and state-space equations are used exclusively in computer computation and op-amp circuit implementation. Thus, thestudents' time is focused on learning only what can be immediately used. Including an author commentary on the best way to approach the text, Signals and Systems, 3/e, is ideal for sophomore- and junior-level undergraduate courses in systems and signals. It assumes a background in general physics (including simple circuit analysis), simple matrix operations, and basiccalculus.

Author Biography

CHI-TSONG CHEN is Professor of Electrical Engineering at the State University of New York at Stony Brook and a Fellow of the IEEE. He is the author of more than eighty technical articles and five books, including Digital Signal Processing (OUP, 2001) and Linear System Theory and Design, 3/e (OUP, 1999).

Preface

xiii

1 Signals

(48)

1.1 Introduction

(1)

1.2 Continuous-Time (CT), Discrete-Time (DT), and Digital Signals

(6)

1.3 Elementary CT Signals

(3)

1.4 Manipulations of CT Signals

(6)

1.4.1 Shifting and Flipping

(2)

1.4.2 Multiplication and Addition

(1)

1.4.3 Modulation

(1)

1.4.4 Windows and Pulses

(2)

1.5 Impulse

(5)

1.5.1 Piecewise-Constant Approximation of CT Signals

(1)

1.6 Elementary DT Signals and Their Manipulation

(5)

1.7 CT Sinusoidal Signals

(8)

1.7.1 Frequency Components

(1)

1.7.2 Complex Exponentials-Positive and Negative Frequencies

(1)

1.7.3 Magnitudes and Phases; Even and Odd

(5)

1.8 DT Sinusoidal Sequences and Nyquist Frequency Range

(6)

1.9 Sampling and Frequency Aliasing

(4)

Problems

(5)

2 Systems

(34)

2.1 Introduction

(1)

2.2 CT Systems with and without Memory

(2)

2.3 The Concept of State-Set of Initial Conditions

(3)

2.3.1 Zero-Input Response and Zero-State Response

(1)

2.4 Linearity of Memoryless Systems

(5)

2.4.1 Linearity of Systems with Memory

(3)

2.5 Time Invariance and Its Implication

(2)

2.6 Implications of Linearity and Time Invariance-Zero-State Responses

(4)

2.7 Modeling CT LTI Lumped Systems

(1)

2.8 Ideal Operational Amplifiers

(6)

2.8.1 DAC and ADC

(2)

2.8.2 A More Realistic Model

(1)

2.9 Ideal Diodes and Rectifiers

(1)

2.10 Discrete-Time LTI Systems

(3)

2.11 Conclusion

(1)

Problems

(5)

3 Convolutions, Difference, and Differential Equations

(33)

3.1 Introduction

(1)

3.1.1 Preliminary

(1)

3.2 DT Impulse Responses

(3)

3.2.1 FIR and IIR Systems

(1)

3.3 DT LTI Systems-Discrete Convolutions

(5)

3.3.1 Underlying Procedure of Discrete Convolutions

(2)

3.4 DT LTI Lumped Systems-Difference Equations

(4)

3.4.1 Setting Up Difference Equations

(1)

3.4.2 From Difference Equations to Convolutions

(2)

3.5 Comparison of Discrete Convolutions and Difference Equations

(1)

3.6 General Forms of Difference Equations

(3)

3.6.1 Recursive and Nonrecursive Difference Equations

(2)

3.7 CT LTI Systems-Integral Convolutions

(5)

3.7.1 Impulse Responses and Step Responses

100

(2)

3.7.2 Graphical Computation of Convolutions

102

(2)

3.8 CT LTI Lumped Systems-Differential Equations

104

(8)

3.8.1 Setting Up Differential Equations

106

(5)

3.8.2 Op-Amp Circuits

111

(1)

Problems

112

(4)

4 Frequency Spectra of CT Signals

116

(36)

4.1 Introduction

116

(2)

4.1.1 Orthogonality of Complex Exponentials

116

(2)

4.2 Fourier Series of Periodic Signals-Frequency Components

118

(8)

4.2.1 Properties of Fourier Series Coefficients

123

(2)

4.2.2 Distribution of Average Power in Frequencies

125

(1)

4.3 Fourier Transform-Frequency Spectra

126

(9)

4.4 Properties of Frequency Spectra

135

(7)

4.4.1 Distribution of Energy in Frequencies

140

(2)

4.5 Frequency Spectra of CT Periodic Signals

142

(3)

4.6 Effects of Truncation

145

(3)

4.7 Time-Limited Band-Limited Theorem

148

(1)

Problems

149

(3)

5 Sampling Theorem and FFT Spectral Computation

152

(38)

5.1 Introduction

152

(1)

5.2 Frequency Spectra of DT Signals-DT Fourier Transform

153

(7)

5.2.1 Nyquist Frequency Range

157

(1)

5.2.2 Inverse DT Fourier Transform

158

(1)

5.2.3 Frequency Spectra of DT Sinusoidal Sequences

159

(1)

5.3 Nyquist Sampling Theorem

160

(10)

5.3.1 Frequency Aliasing Due to Time Sampling

164

(4)

5.3.2 Construction of CT Signals from DT Signals

168

(2)

5.4 Computing Frequency Spectra of DT Signals

170

(3)

5.4.1 Fast Fourier Transform (FFT)

171

(2)

5.5 FFT Spectral Computation of DT Signals

173

(6)

5.5.1 Interpolation and Frequency Resolution

174

(3)

5.5.2 Plotting Spectra in {-π/Τ,π/Τ)

177

(2)

5.6 FFT Spectral Computation of CT Signals

179

(9)

5.6.1 Selecting T and N

184

(3)

5.6.2 FFT Spectral Computation of CT Sinusoids

187

(1)

Problems

188

(2)

6 CT Transfer Functions-Laplace Transform

190

(65)

6.1 Introduction

190

(1)

6.2 Laplace Transform

190

(4)

6.3 Transfer Functions

194

(9)

6.3.1 From Differential Equations to Rational Transfer Functions

195

(3)

6.3.2 Transform Impedances

198

(2)

6.3.3 Proper Rational Transfer Functions

200

(1)

6.3.4 Poles and Zeros

201

(2)

6.4 Properties of Laplace Transform

203

(4)

6.5 Inverse Laplace Transform

207

(10)

6.5.1 Real Simple Poles

208

(3)

6.5.2 Repeated Real Poles

211

(2)

6.5.3 Simple Complex Poles-Quadratic Terms

213

(1)

6.5.4 Why Transfer Functions Are Not Used in Computer Computation

214

(1)

6.5.5 A Study of Automobile Suspension Systems

215

(2)

6.6 Significance of Poles and Zeros

217

(3)

6.7 Stability

220

(9)

6.7.1 Routh Test

226

(3)

6.8 Frequency Responses

229

(10)

6.8.1 Speed of Response-Time Constant

235

(2)

6.8.2 Bandwidth of Frequency-Selective Filters

237

(1)

6.8.3 An Alternative Derivation of Frequency Responses

238

(1)

6.9 From Laplace Transform to Fourier Transform

239

(10)

6.9.1 Why Fourier Transform Is Not Used in System Analysis

242

(1)

6.9.2 Phasor Analysis

243

(1)

6.10 Frequency Responses and Frequency Spectra

244

(1)

6.10.1 Resonance

245

(3)

6.11 Concluding Remarks

248

(1)

Problems

249

(6)

7 Realizations, Characterization, and Identification

255

(42)

7.1 Introduction

255

(1)

7.2 Realizations

256

(6)

7.2.1 Minimal Realizations

261

(1)

7.3 Basic Block Diagrams

262

(7)

7.3.1 Op-Amp Circuit Implementations

264

(2)

7.3.2 Stability of Op-Amp Circuits

266

(3)

7.4 Computer Computation of State-Space Equations

269

(4)

7.4.1 MATLAB Computation

270

(3)

7.5 Developing State-Space Equations

273

(7)

7.5.1 From State-Space Equations to Transfer Functions

278

(2)

7.6 Complete Characterization by Transfer Functions

280

(5)

7.6.1 Can We Disregard Zero-Input Responses?

283

(2)

7.7 Identification by Measuring Frequency Responses

285

(6)

7.7.1 Models of Op Amps

289

(1)

7.7.2 Measuring Frequency Responses Using Sweep Sinusoids

290

(1)

Problems

291

(6)

8 Model Reduction, Feedback, and Modulation

297

(40)

8.1 Introduction

297

(1)

8.2 Op-Amp Circuits Using a Single-Pole Model

297

(5)

8.2.1 Model Reduction-Operational Frequency Range

299

(3)

8.3 Seismometers and Accelerometers

302

(7)

8.4 Composite Systems

309

(10)

8.4.1 Loading Problem

310

(2)

8.4.2 Why Feedback?

312

(2)

8.4.3 Stability of Feedback Systems

314

(2)

8.4.4 Inverse Systems

316

(3)

8.5 Wien-Bridge Oscillator

319

(3)

8.6 Feedback Model of Op-Amp Circuits

322

(2)

8.6.1 Feedback Model of Wien-Bridge Oscillator

323

(1)

8.7 Modulation

324

(6)

8.7.1 Filtering and Synchronous Demodulation

326

(4)

8.8 AM Modulation and Asynchronous Demodulation

330

(3)

Problems

333

(4)

9 DT Transfer Functions-z-Transform

337

(43)

9.1 Introduction

337

(1)

9.2 z-Transform

338

(4)

9.2.1 From Laplace Transform to z-Transform

341

(1)

9.3 DT Transfer Functions

342

(8)

9.3.1 From Difference Equations to Rational Transfer Functions

343

(5)

9.3.2 Poles and Zeros

348

(1)

9.3.3 Transfer Functions of FIR and IIR Systems

349

(1)

9.4 Properties of z-Transform

350

(3)

9.5 Inverse z-Transform

353

(4)

9.6 Significance of Poles and Zeros

357

(3)

9.7 Stability

360

(7)

9.7.1 Jury Test

364

(3)

9.8 Frequency Responses

367

(7)

9.8.1 Speed of Response-Time Constant

372

(2)

9.9 Frequency Responses and Frequency Spectra

374

(2)

9.10 Digital Processing of CT Signals

376

(1)

Problems

377

(3)

10 DT State-Space Equations and Realizations

380

(19)

10.1 Introduction

380

(1)

10.2 From Difference Equations to Basic Block Diagrams

380

(1)

10.2.1 Basic Block Diagrams to State-Space Equations

383

(1)

10.3 Realizations

384

(1)

10.3.1 Minimal Realizations

389

(2)

10.4 MATLAB Computation

391

(1)

10.4.1 MATLAB Computation of Convolutions

395

(1)

10.5 Complete Characterization by Transfer Functions

396

(1)

Problems

397

(2)

References

399

(2)

Answers to Selected Problems

401

(16)

Index

417

Signals and Systems

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