Preface 1
1 FUNDAMENTAL CONCEPTS 1
1.1 Signals and Systems 1
1.2 Continuous-Time Signals 6
1.3 Discrete-Time Signals 17
1.4 Examples of Systems 25
1.5 Basic System Properties 36
Problems 47
2 SYSTEMS DEFINED BY DIFFERENTIAL OR DIFFERENCE EOUATIONS 57
2.1 Linear Input/Output Differential Equations with Constant Coefficients 57
2.2 System Modeling 61
2.3 Linear Input/Output Difference Equations with Constant Coefficients 66
2.4 Discretization in Time of Differential Equations 72
2.5 Systems Defined by Time-Varying or Nonlinear Equations 80
Problems 88
3 CONVOLUTION REPRESENTATION 101
3.1 Convolution Representation of Linear Time-Invariant Discrete-Time Systems 101
3.2 Convolution of Discrete-Time Signals 104
3.3 Convolution Representation of Linear Time-Invariant Continuous-Time Systems 114
3.4 Convolution of Continuous-Time Signals 118
3.5 Numerical Convolution 128
3.6 Linear Time-Varying Systems 132
Problems 134
4 THE FOURIER SERIES AND FOURIER TRANSFORM 145
4.1 Representation of Signals in Terms of Frequency Components 146
4.2 Fourier Series Representation of Periodic Signals 153
4.3 Fourier Transform 161
4.4 Properties of the Fourier Transform 175
4.5 Generalized Fourier Transform 190
Problems 193
5 FREQUENCY-DOMAIN ANALYSIS OF SYSTEMS 202
5.1 Response to a Sinusoidal Input 203
5.2 Response to Periodic Inputs 210
5.3 Response to Aperiodic Inputs 216
5.4 Analysis of Ideal Filters 221
5.5 Sampling 231
Problems 238
6 APPLICATION TO COMMUNICATIONS 251
6.1 Analog Modulation 252
6.2 Demodulation of Analog Signals 260
6.3 Simultaneous Transmission of Signals 264
6.4 Digital Modulation 268
6.5 Baseband PAM 272
6.6 Passband PAM 276
6.7 Digital Communication Simulations 282
Problems 289
7 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS 297
7.1 Discrete-Time Fourier Transform 298
7.2 Discrete Fourier Transform 310
7.3 Properties of the DFT 322
7.4 System Analysis via the DTFT and DFT 331
7.5 FFT Algorithm 339
7.6 Applications of the FFT Algorithm 341
Problems 349
8 THE LAPLACE TRANSFORM AND THE TRANSFER FUNCTION REPRESENTATION 358
8.1 Laplace Transform of a Signal 359
8.2 Properties of the Laplace Transform 363
8.3 Computation of the Inverse Laplace Transform 374
8.4 Transform of the Input/Output Differential Equation 394
8.5 Transfer Function Representation 401
8.6 Transfer Function of Block Diagrams 415
Problems 423
9 SYSTEM ANALYSIS USING THE TRANSFER FUNCTION REPRESENTATION 435
9.1 Stability and the Impulse Response 436
9.2 Routh-Hurwitz Stability Test 439
9.3 Analysis of the Step Response 443
9.4 Response to Sinusoids and Arbitrary Inputs 459
9.5 Frequency Response Function 465
9.6 Causal Filters 484
Problems 498
10 APPLICATION TO CONTROL 509
10.1 Introduction to Control 509
10.2 Tracking Control 516
10.3 Root Locus 527
10.3 Application to Control System Design 535
Problems 543
11 THE z-TRANSFORM AND DISCRETE-TIME SYSTEMS 555
11.1 z-Transform of a Discrete-Time Signal 556
11.2 Properties of the z-Transform 560
11.3 Computation of the Inverse z-Transform 571
11.4 Transfer Function Representation 581
11.5 Stability of Discrete-Time Systems 593
11.6 Frequency Response of Discrete-Time Systems 597
Problems 601
12 DESIGN OF DIGITAL FILTERS AND CONTROLLERS 612
12.1 Discretization 613
12.2 Design of IIR Filters 618
12.3 Design of IIR Filters Using MATLAB 623
12.4 Design of FIR Filters 630
12.5 Design of Digital Controllers 643
Problems 649
13 STATE REPRESENTATION 655
13.1 State Model 656
13.2 Construction of State Models 659
13.3 Solution of State Equations 667
13.4 Discrete-Time Systems 676
13.5 Equivalent State Representations 683
13.6 Discretization of State Model 689
Problems 692
APPENDIX A BRIEF REVIEW OF COMPLEX VARIABLES 703
APPENDIX B BRIEF REVIEW OF MATRICES 708
BIBLIOGRAPHY 714
INDEX 717