Part Ⅰ Introduction to signals and systems 1
1 Introduction to signals 3
1.1 Classification of signals 5
1.2 Elementary signals 25
1.3 Signal operations 35
1.4 Signal implementation with MATLAB 47
1.5 Summary 51
Problems 53
2 Introduction to systems 62
2.1 Examples of systems 63
2.2 Classification of systems 72
2.3 Interconnection of systems 90
2.4 Summary 93
Problems 94
Part Ⅱ Continuous-time signals and systems 101
3 Time-domain analysis of LTIC systems 103
3.1 Representation of LTIC systems 103
3.2 Representation of signals using Dirac delta functions 112
3.3 Impulse response of a system 113
3.4 Convolution integral 116
3.5 Graphical method for evaluating the convolution integral 118
3.6 Properties of the convolution integral 125
3.7 Impulse response of LTIC systems 127
3.8 Experiments with MATLAB 131
3.9 Summary 135
Problems 137
4 Signal representation using Fourier series 141
4.1 Orthogonal vector space 142
4.2 Orthogonal signal space 143
4.3 Fourier basis functions 149
4.4 Trigonometric CTFS 153
4.5 Exponential Fourier series 163
4.6 Properties of exponential CTFS 169
4.7 Existence of Fourier series 177
4.8 Application of Fourier series 179
4.9 Summary 182
Problems 184
5 Continuous-time Fourier transform 193
5.1 CTFT for aperiodic signals 193
5.2 Examples of CTFT 196
5.3 Inverse Fourier transform 209
5.4 Fourier transform of real,even,and odd functions 211
5.5 Properties of the CTFT 216
5.6 Existence of the CTFT 231
5.7 CTFT of periodic functions 233
5.8 CTFS coefficients as samples of CTFT 235
5.9 LTIC systems analysis using CTFT 237
5.10 MATLAB exercises 246
5.11 Summary 251
Problems 253
6 Laplace transform 261
6.1 Analytical development 262
6.2 Unilateral Laplace transform 266
6.3 Inverse Laplace transform 273
6.4 Properties of the Laplace transform 276
6.5 Solution of differential equations 288
6.6 Characteristic equation,zeros,and poles 293
6.7 Properties of the ROC 295
6.8 Stable and causal LTIC systems 298
6.9 LTIC systems analysis using Laplace transform 305
6.10 Block diagram representations 307
6.11 Summary 311
Problems 313
7 Continuous-time filters 320
7.1 Filter classification 321
7.2 Non-ideal filter characteristics 324
7.3 Design of CT lowpass filters 327
7.4 Frequency transformations 352
7.5 Summary 364
Problems 365
8 Case studies for CT systems 368
8.1 Amplitude modulation of baseband signals 369
8.2 Mechanical spring damper system 374
8.3 Armature-controlled dc motor 377
8.4 Immune system in humans 383
8.5 Summary 388
Problems 388
Part Ⅲ Discrete-time signals and systems 391
9 Sampling and quantization 393
9.1 Ideal impulse-train sampling 395
9.2 Practical approaches to sampling 405
9.3 Quantization 410
9.4 Compact disks 413
9.5 Summary 415
Problems 416
10 Time-domain analysis of discrete-time systems systems 422
10.1 Finite-difference equation representation of LTID systems 423
10.2 Representation of sequences using Dirac delta functions 426
10.3 Impulse response of a system 427
10.4 Convolution sum 430
10.5 Graphical method for evaluating the convolution sum 432
10.6 Periodic convolution 439
10.7 Properties of the convolution sum 448
10.8 Impulse response of LTID systems 451
10.9 Experiments with MATLAB 455
10.10 Summary 459
Problems 460
11 Discrete-time Fourier series and transform 464
11.1 Discrete-time Fourier series 465
11.2 Fourier transform for aperiodic functions 475
11.3 Existence of the DTFT 482
11.4 DTFT of periodic functions 485
11.5 Properties of the DTFT and the DTFS 491
11.6 Frequency response of LTID systems 506
11.7 Magnitude and phase spectra 507
11.8 Continuous-and discrete-time Fourier transforms 514
11.9 Summary 517
Problems 520
12 Discrete Fourier transform 525
12.1 Continuous to discrete Fourier transform 526
12.2 Discrete Fourier transform 531
12.3 Spectrum analysis using the DFT 538
12.4 Properties of the DFT 547
12.5 Convolution using the DFT 550
12.6 Fast Fourier transform 553
12.7 Summary 559
Problems 560
13 The z-transform 565
13.1 Analytical development 566
13.2 Unilateral z-transform 569
13.3 Inverse z-transform 574
13.4 Properties of the z-transform 582
13.5 Solution of difference equations 594
13.6 z-transfer function of LTID systems 596
13.7 Relationship between Laplace and z-transforms 599
13.8 Stabilty analysis in the z-domain 601
13.9 Frequency-response calculation in the z-domain 606
13.10 DTFT and the z-transform 607
13.11 Experiments with MATLAB 609
13.12 Summary 614
Problems 616
14 Digital filters 621
14.1 Filter classification 622
14.2 FIR and IIR filters 625
14.3 Phase of a digital filter 627
14.4 Ideal versus non-ideal filters 632
14.5 Filter realization 638
14.6 FIR filters 639
14.7 IIR filters 644
14.8 Finite precision effect 651
14.9 MATLAB examples 657
14.10 Summary 658
Problems 660
15 FIR filter design 665
15.1 Lowpass filter design using windowing method 666
15.2 Design of highpass filters using windowing 684
15.3 Design of bandpass filters using windowing 688
15.4 Design of a bandstop filter using windowing 691
15.5 Optimal FIR filters 693
15.6 MATLAB examples 700
15.7 Summary 707
Problems 709
16 IIR filter design 713
16.1 IIR filter design principles 714
16.2 Impulse invariance 715
16.3 Bilinear transformation 728
16.4 Designing highpass,bandpass,and bandstop IIR filters 734
16.5 IIR and FIR filters 737
16.6 Summary 741
Problems 742
17 Applications of digital signal processing 746
17.1 Spectral estimation 746
17.2 Digital audio 754
17.3 Audio filtering 759
17.4 Digital audio compression 765
17.5 Digital images 771
17.6 Image filtering 777
17.7 Image compression 782
17.8 Summary 789
Problems 789
Appendix A Mathematical preliminaries 793
A.1 Trigonometric identities 793
A.2 Power series 794
A.3 Series summation 794
A.4 Limits and differential calculus 795
A.5 Indefinite integrals 795
Appendix B Introducion to the complex-number system 797
B.1 Real-number system 797
B.2 Complex-number system 798
B.3 Graphical interpertation of complex numbers 801
B.4 Polar representation of complex numbers 801
B.5 Summary 805
Problems 805
Appendix C Linear constant-coefficient differential equations 806
C.1 Zero-input response 807
C.2 Zero-state response 810
C.3 Complete response 813
Appendix D Partial fraction expansion 814
D.1 Laplace transform 814
D.2 Continuous-time Fourier transform 822
D.3 Discrete-time Fourier transform 825
D.4 The z-transform 826
Appendix E Introduction to MATLAB 829
E.1 Introduction 829
E.2 Entering data into MATLAB 831
E.3 Control statements 838
E.4 Elementary matrix operations 840
E.5 Plotting functions 842
E.6 Creating MATLAB functions 846
E.7 Summary 847
Appendix F About the CD 848
F.1 Interactive environment 848
F.2 Data 853
F.3 MATLAB codes 854
Bibliography 858
Index 860