Signals and Systems - Using MATLAB Electrical Engineering PDF BOOK DOWNLOAD
Contents
PREFACE..................................................................................................................... xi
ACKNOWLEDGMENTS ................................................................................................ xvi
Part 1 Introduction 1
CHAPTER 0 From the Ground Up!............................................................................. 3
0.1 Signals and Systems and Digital Technologies........................................ 3
0.2 Examples of Signal Processing Applications ........................................... 5
0.2.1 Compact-Disc Player ................................................................ 5
0.2.2 Software-Defined Radio and Cognitive Radio............................... 6
0.2.3 Computer-Controlled Systems ................................................... 8
0.3 Analog or Discrete? ............................................................................. 9
0.3.1 Continuous-Time and Discrete-Time Representations .................. 10
0.3.2 Derivatives and Finite Differences ............................................. 12
0.3.3 Integrals and Summations......................................................... 13
0.3.4 Differential and Difference Equations ......................................... 16
0.4 Complex or Real? ................................................................................ 20
0.4.1 Complex Numbers and Vectors.................................................. 20
0.4.2 Functions of a Complex Variable................................................ 23
0.4.3 Phasors and Sinusoidal Steady State .......................................... 24
0.4.4 Phasor Connection ................................................................... 26
0.5 Soft Introduction to MATLAB ............................................................... 29
0.5.1 Numerical Computations .......................................................... 30
0.5.2 Symbolic Computations ............................................................ 43
Problems............................................................................................ 53
Part 2 Theory and Application of Continuous-Time
Signals and Systems 63
CHAPTER 1 Continuous-Time Signals ......................................................................... 65
1.1 Introduction ....................................................................................... 65
1.2 Classification of Time-Dependent Signals............................................... 66
iv
Contents v
1.3 Continuous-Time Signals ..................................................................... 67
1.3.1 Basic Signal Operations—Time Shifting and Reversal................... 71
1.3.2 Even and Odd Signals .............................................................. 75
1.3.3 Periodic and Aperiodic Signals .................................................. 77
1.3.4 Finite-Energy and Finite Power Signals ...................................... 79
1.4 Representation Using Basic Signals....................................................... 85
1.4.1 Complex Exponentials.............................................................. 85
1.4.2 Unit-Step, Unit-Impulse, and Ramp Signals ................................. 88
1.4.3 Special Signals—the Sampling Signal and the Sinc ....................... 100
1.4.4 Basic Signal Operations—Time Scaling, Frequency Shifting,
and Windowing ....................................................................... 102
1.4.5 Generic Representation of Signals.............................................. 105
1.5 What Have We Accomplished? Where Do We Go from Here?.................... 106
Problems............................................................................................ 108
CHAPTER 2 Continuous-Time Systems ....................................................................... 117
2.1 Introduction ....................................................................................... 117
2.2 System Concept .................................................................................. 118
2.2.1 System Classification................................................................ 118
2.3 LTI Continuous-Time Systems .............................................................. 119
2.3.1 Linearity ................................................................................. 120
2.3.2 Time Invariance....................................................................... 125
2.3.3 Representation of Systems by Differential Equations.................... 130
2.3.4 Application of Superposition and Time Invariance ....................... 135
2.3.5 Convolution Integral................................................................. 136
2.3.6 Causality ................................................................................ 143
2.3.7 Graphical Computation of Convolution Integral ........................... 145
2.3.8 Interconnection of Systems—Block Diagrams .............................. 147
2.3.9 Bounded-Input Bounded-Output Stability ................................... 153
2.4 What Have We Accomplished? Where Do We Go from Here?.................... 156
Problems............................................................................................ 157
CHAPTER 3 The Laplace Transform ............................................................................ 165
3.1 Introduction ....................................................................................... 165
3.2 The Two-Sided Laplace Transform ........................................................ 166
3.2.1 Eigenfunctions of LTI Systems................................................... 167
3.2.2 Poles and Zeros and Region of Convergence ............................... 172
3.3 The One-Sided Laplace Transform ........................................................ 176
3.3.1 Linearity ................................................................................. 185
3.3.2 Differentiation ......................................................................... 188
3.3.3 Integration .............................................................................. 193
3.3.4 Time Shifting........................................................................... 194
3.3.5 Convolution Integral................................................................. 196
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3.4 Inverse Laplace Transform ................................................................... 197
3.4.1 Inverse of One-Sided Laplace Transforms ................................... 197
3.4.2 Inverse of Functions Containing e
−ρs Terms ................................ 209
3.4.3 Inverse of Two-Sided Laplace Transforms................................... 212
3.5 Analysis of LTI Systems ....................................................................... 214
3.5.1 LTI Systems Represented by Ordinary Differential Equations ........ 214
3.5.2 Computation of the Convolution Integral .................................... 221
3.6 What Have We Accomplished? Where Do We Go from Here?.................... 226
Problems............................................................................................ 226
CHAPTER 4 Frequency Analysis: The Fourier Series .................................................. 237
4.1 Introduction ....................................................................................... 237
4.2 Eigenfunctions Revisited ..................................................................... 238
4.3 Complex Exponential Fourier Series ...................................................... 245
4.4 Line Spectra ....................................................................................... 248
4.4.1 Parseval’s Theorem—Power Distribution over Frequency ............. 248
4.4.2 Symmetry of Line Spectra ......................................................... 250
4.5 Trigonometric Fourier Series ................................................................ 251
4.6 Fourier Coefficients from Laplace.......................................................... 255
4.7 Convergence of the Fourier Series......................................................... 265
4.8 Time and Frequency Shifting................................................................ 270
4.9 Response of LTI Systems to Periodic Signals........................................... 273
4.9.1 Sinusoidal Steady State............................................................. 274
4.9.2 Filtering of Periodic Signals....................................................... 276
4.10 Other Properties of the Fourier Series .................................................... 279
4.10.1 Reflection and Even and Odd Periodic Signals ............................. 279
4.10.2 Linearity of Fourier Series—Addition of Periodic Signals............... 282
4.10.3 Multiplication of Periodic Signals ............................................... 284
4.10.4 Derivatives and Integrals of Periodic Signals ............................... 285
4.11 What Have We Accomplished? Where Do We Go from Here?.................... 289
Problems............................................................................................ 290
CHAPTER 5 Frequency Analysis: The Fourier Transform ........................................... 299
5.1 Introduction ....................................................................................... 299
5.2 From the Fourier Series to the Fourier Transform .................................... 300
5.3 Existence of the Fourier Transform ....................................................... 302
5.4 Fourier Transforms from the Laplace Transform ..................................... 302
5.5 Linearity, Inverse Proportionality, and Duality ........................................ 304
5.5.1 Linearity ................................................................................. 304
5.5.2 Inverse Proportionality of Time and Frequency............................ 305
5.5.3 Duality ................................................................................... 310
Contents vii
5.6 Spectral Representation ....................................................................... 313
5.6.1 Signal Modulation .................................................................... 313
5.6.2 Fourier Transform of Periodic Signals ......................................... 317
5.6.3 Parseval’s Energy Conservation................................................. 320
5.6.4 Symmetry of Spectral Representations........................................ 322
5.7 Convolution and Filtering..................................................................... 327
5.7.1 Basics of Filtering .................................................................... 329
5.7.2 Ideal Filters............................................................................. 332
5.7.3 Frequency Response from Poles and Zeros.................................. 337
5.7.4 Spectrum Analyzer................................................................... 341
5.8 Additional Properties .......................................................................... 344
5.8.1 Time Shifting .......................................................................... 344
5.8.2 Differentiation and Integration .................................................. 346
5.9 What Have We Accomplished? What Is Next? ....................................... 350
Problems............................................................................................ 350
CHAPTER 6 Application to Control and Communications ........................................... 359
6.1 Introduction ....................................................................................... 359
6.2 System Connections and Block Diagrams ............................................... 360
6.3 Application to Classic Control............................................................... 363
6.3.1 Stability and Stabilization ......................................................... 369
6.3.2 Transient Analysis of First- and Second-Order Control Systems ..... 371
6.4 Application to Communications ............................................................ 377
6.4.1 AM with Suppressed Carrier ..................................................... 379
6.4.2 Commercial AM....................................................................... 380
6.4.3 AM Single Sideband ................................................................. 382
6.4.4 Quadrature AM and Frequency-Division Multiplexing .................. 383
6.4.5 Angle Modulation .................................................................... 385
6.5 Analog Filtering.................................................................................. 390
6.5.1 Filtering Basics........................................................................ 390
6.5.2 Butterworth Low-Pass Filter Design........................................... 393
6.5.3 Chebyshev Low-Pass Filter Design ............................................ 396
6.5.4 Frequency Transformations ...................................................... 402
6.5.5 Filter Design with MATLAB ...................................................... 405
6.6 What Have We Accomplished? What Is Next? ........................................ 409
Problems............................................................................................ 409
Part 3 Theory and Application of Discrete-Time
Signals and Systems 417
CHAPTER 7 Sampling Theory...................................................................................... 419
7.1 Introduction ....................................................................................... 419
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7.2 Uniform Sampling ............................................................................... 420
7.2.1 Pulse Amplitude Modulation ..................................................... 420
7.2.2 Ideal Impulse Sampling ............................................................ 421
7.2.3 Reconstruction of the Original Continuous-Time Signal ................ 428
7.2.4 Signal Reconstruction from Sinc Interpolation.............................. 432
7.2.5 Sampling Simulation with MATLAB ........................................... 433
7.3 The Nyquist-Shannon Sampling Theorem .............................................. 437
7.3.1 Sampling of Modulated Signals.................................................. 438
7.4 Practical Aspects of Sampling............................................................... 439
7.4.1 Sample-and-Hold Sampling ....................................................... 439
7.4.2 Quantization and Coding .......................................................... 441
7.4.3 Sampling, Quantizing, and Coding with MATLAB........................ 444
7.5 What Have We Accomplished? Where Do We Go from Here?.................... 446
Problems............................................................................................ 447
CHAPTER 8 Discrete-Time Signals and Systems ......................................................... 451
8.1 Introduction ..................................................................................... 451
8.2 Discrete-Time Signals.......................................................................... 452
8.2.1 Periodic and Aperiodic Signals .................................................. 454
8.2.2 Finite-Energy and Finite-Power Discrete-Time Signals ................. 458
8.2.3 Even and Odd Signals .............................................................. 461
8.2.4 Basic Discrete-Time Signals ...................................................... 465
8.3 Discrete-Time Systems ........................................................................ 478
8.3.1 Recursive and Nonrecursive Discrete-Time Systems..................... 481
8.3.2 Discrete-Time Systems Represented by Difference
Equations ............................................................................... 486
8.3.3 The Convolution Sum ............................................................... 487
8.3.4 Linear and Nonlinear Filtering with MATLAB.............................. 494
8.3.5 Causality and Stability of Discrete-Time Systems ......................... 497
8.4 What Have We Accomplished? Where Do We Go from Here?.................... 502
Problems............................................................................................ 502
CHAPTER 9 The Z-Transform ...................................................................................... 511
9.1 Introduction ....................................................................................... 511
9.2 Laplace Transform of Sampled Signals................................................... 512
9.3 Two-Sided Z-Transform ....................................................................... 515
9.3.1 Region of Convergence............................................................. 516
9.4 One-Sided Z-Transform........................................................................ 521
9.4.1 Computing the Z-Transform with Symbolic MATLAB ................... 522
9.4.2 Signal Behavior and Poles ......................................................... 522
9.4.3 Convolution Sum and Transfer Function ..................................... 526
Contents ix
9.4.4 Interconnection of Discrete-Time Systems................................... 537
9.4.5 Initial and Final Value Properties ............................................... 539
9.5 One-Sided Z-Transform Inverse ............................................................ 542
9.5.1 Long-Division Method .............................................................. 542
9.5.2 Partial Fraction Expansion ........................................................ 544
9.5.3 Inverse Z-Transform with MATLAB............................................ 547
9.5.4 Solution of Difference Equations ................................................ 550
9.5.5 Inverse of Two-Sided Z-Transforms............................................ 561
9.6 What Have We Accomplished? Where Do We Go from Here?.................... 564
Problems............................................................................................ 564
CHAPTER 10 Fourier Analysis of Discrete-Time Signals and Systems........................... 571
10.1 Introduction ....................................................................................... 571
10.2 Discrete-Time Fourier Transform .......................................................... 572
10.2.1 Sampling, Z-Transform, Eigenfunctions, and the DTFT ................. 573
10.2.2 Duality in Time and Frequency .................................................. 575
10.2.3 Computation of the DTFT Using MATLAB .................................. 577
10.2.4 Time and Frequency Supports ................................................... 580
10.2.5 Parseval’s Energy Result........................................................... 585
10.2.6 Time and Frequency Shifts........................................................ 587
10.2.7 Symmetry ............................................................................... 589
10.2.8 Convolution Sum ..................................................................... 595
10.3 Fourier Series of Discrete-Time Periodic Signals...................................... 596
10.3.1 Complex Exponential Discrete Fourier Series .............................. 599
10.3.2 Connection with the Z-Transform .............................................. 601
10.3.3 DTFT of Periodic Signals........................................................... 602
10.3.4 Response of LTI Systems to Periodic Signals ............................... 604
10.3.5 Circular Shifting and Periodic Convolution .................................. 607
10.4 Discrete Fourier Transform .................................................................. 614
10.4.1 DFT of Periodic Discrete-Time Signals ........................................ 614
10.4.2 DFT of Aperiodic Discrete-Time Signals...................................... 616
10.4.3 Computation of the DFT via the FFT .......................................... 617
10.4.4 Linear and Circular Convolution Sums ........................................ 622
10.5 What Have We Accomplished? Where Do We Go from Here?.................... 628
Problems............................................................................................ 629
CHAPTER 11 Introduction to the Design of Discrete Filters .......................................... 639
11.1 Introduction ....................................................................................... 639
11.2 Frequency-Selective Discrete Filters...................................................... 641
11.2.1 Linear Phase ........................................................................... 641
11.2.2 IIR and FIR Discrete Filters ....................................................... 643
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11.3 Filter Specifications ............................................................................. 648
11.3.1 Frequency-Domain Specifications .............................................. 648
11.3.2 Time-Domain Specifications ...................................................... 652
11.4 IIR Filter Design.................................................................................. 653
11.4.1 Transformation Design of IIR Discrete Filters .............................. 654
11.4.2 Design of Butterworth Low-Pass Discrete Filters ......................... 658
11.4.3 Design of Chebyshev Low-Pass Discrete Filters........................... 666
11.4.4 Rational Frequency Transformations .......................................... 672
11.4.5 General IIR Filter Design with MATLAB ..................................... 677
11.5 FIR Filter Design ................................................................................. 679
11.5.1 Window Design Method ........................................................... 681
11.5.2 Window Functions ................................................................... 683
11.6 Realization of Discrete Filters ............................................................... 689
11.6.1 Realization of IIR Filters............................................................ 690
11.6.2 Realization of FIR Filters ........................................................... 699
11.7 What Have We Accomplished? Where Do We Go from Here?.................... 701
Problems............................................................................................ 701
CHAPTER 12 Applications of Discrete-Time Signals and Systems................................. 709
12.1 Introduction ....................................................................................... 709
12.2 Application to Digital Signal Processing................................................. 710
12.2.1 Fast Fourier Transform ............................................................. 711
12.2.2 Computation of the Inverse DFT ................................................ 715
12.2.3 General Approach of FFT Algorithms ......................................... 716
12.3 Application to Sampled-Data and Digital Control Systems ........................ 722
12.3.1 Open-Loop Sampled-Data System .............................................. 724
12.3.2 Closed-Loop Sampled-Data System ............................................ 726
12.4 Application to Digital Communications.................................................. 729
12.4.1 Pulse Code Modulation............................................................. 730
12.4.2 Time-Division Multiplexing ....................................................... 733
12.4.3 Spread Spectrum and Orthogonal Frequency-Division
Multiplexing............................................................................ 735
12.5 What Have We Accomplished? Where Do We Go from Here?.................... 742
APPENDIX Useful Formulas....................................................................................... 743
BIBLIOGRAPHY ........................................................................................................... 746
INDEX ......................................................................................................................... 749
