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 |  موضوع: كتاب Signals and Systems Laboratory with MATLAB الأحد 24 مارس 2024, 1:43 am | |
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أخواني في الله
أحضرت لكم كتاب
Signals and Systems Laboratory with MATLAB
Alex Palamides, Anastasia Veloni
و المحتوى كما يلي :
Contents
Preface . xiii
Authors xvii
1. Introduction to MATLAB 1
1.1 What Is MATLAB? . 1
1.2 Working Environment 1
1.3 Getting Started 2
1.3.1 Simple Arithmetic Operations . 3
1.3.2 Comments 3
1.3.3 The Variable ans 3
1.3.4 Priority of Operations 3
1.3.5 Constants 4
1.3.6 Built-In Functions 5
1.3.7 Variables . 6
1.3.8 Format 7
1.3.9 Help in MATLAB 7
1.4 Memory Management . 8
1.4.1 Commands save-load-exit-quit . 9
1.4.2 The Command clear 10
1.5 Commands diary and clc . 10
1.6 Vectors 11
1.6.1 Row Vectors . 11
1.6.2 Commands length=size 11
1.6.3 Addition=Subtraction 12
1.6.4 Multiplication, Division, and Power . 13
1.6.5 Column Vectors . 14
1.6.6 Dot Product of Two Vectors 14
1.6.7 Useful Commands . 15
1.7 Matrices . 16
1.7.1 Matrix Concatenation 17
1.7.2 Working with Matrices . 17
1.7.3 Addition=Subtraction 19
1.7.4 Multiplication of Matrices . 19
1.7.4.1 The Dot Product as a Special Case of Matrix
Multiplication . 21
1.7.5 Power of a Matrix 21
1.7.6 Inverse of a Matrix . 22
1.7.7 Determinant of a Matrix . 22
1.7.8 Division of Matrices . 23
1.7.9 Transpose of a Matrix 24
1.7.10 Special Forms of Matrices . 25
1.7.11 Useful Commands . 26
1.8 Plotting with MATLAB 27
1.8.1 Plotting in Two Dimensions 27
vvi Contents
1.8.2 The Fig File . 29
1.8.3 The Command linspace . 29
1.8.4 Plotting Several Functions in One Figure . 30
1.8.5 Formatting a Figure . 32
1.8.6 Plotting in Different Figures . 34
1.8.7 Commands for Plotting . 36
1.8.8 Plotting Discrete-Time Functions 38
1.8.9 Graph in Polar Coordinates 39
1.8.10 Piecewise Functions . 39
1.8.11 Plotting in Three Dimensions 40
1.8.11.1 Plotting Curves in Three Dimensions . 41
1.8.11.2 Plotting Surfaces in Three Dimensions . 41
1.9 Complex Numbers 43
1.9.1 Useful Commands 43
1.9.2 Forms of Complex Numbers 44
1.9.3 Operations with Complex Numbers 45
1.9.4 Graph of Complex Numbers 46
1.10 M-Files . 48
1.10.1 Scripts 48
1.10.2 Functions . 51
1.11 Input=Output Commands 54
1.12 File Management . 55
1.13 Logical=Relational Operators . 57
1.14 Control Flow . 58
1.15 Symbolic Variables 62
1.15.1 Differentiation of a Function 62
1.15.2 Integration of a Function . 63
1.15.3 Summation of a Function 63
1.15.4 Rational Form . 64
1.15.5 Solving Algebraic Equations 64
1.15.6 Solving Differential Equations . 65
1.15.7 The Command subs 66
1.16 Polynomials . 66
1.17 (Pseudo)Random Numbers 68
1.18 Solved Problems 69
1.19 Homework Problems 75
2. Signals . 77
2.1 Categorization by the Variable Type . 77
2.1.1 Continuous-Time Signals 77
2.1.2 Discrete-Time Signals 78
2.1.3 Digital Signals 79
2.2 Basic Continuous-Time Signals 81
2.2.1 Sinusoidal Signals . 81
2.2.2 Exponential Signals . 82
2.2.3 Complex Exponential Signals 83
2.2.4 Unit Step Function 84
2.2.5 Unit Impulse or Dirac Delta Function . 89Contents vii
2.2.6 Ramp Function . 93
2.2.7 Rectangular Pulse Function 96
2.3 Discrete-Time Signals . 99
2.3.1 Unit Impulse Sequence . 100
2.3.2 Unit Step Sequence 102
2.3.3 Real Exponential Sequence 104
2.3.4 Complex Exponential Sequence 105
2.3.5 Sinusoidal Sequence 109
2.4 Properties of Signals . 111
2.4.1 Periodic Signals 111
2.4.1.1 Sum of Periodic Continuous-Time Signals . 112
2.4.1.2 Construction of Periodic Signals . 114
2.4.2 Causal Signals . 118
2.4.3 Even and Odd Signals . 119
2.4.4 Energy and Power Signals . 121
2.4.5 Deterministic and Stochastic Signals . 124
2.5 Transformations of the Time Variable for Continuous-Time Signals 126
2.5.1 Time Reversal or Reflection . 126
2.5.2 Time Scaling . 127
2.5.3 Time Shifting 129
2.6 Transformations of the Time Variable for Discrete-Time Signals 132
2.7 Solved Problems . 135
2.8 Homework Problems 145
3. Systems . 147
3.1 Systems Classification . 147
3.1.1 Classification according to the Number of Inputs and Outputs 147
3.1.2 Continuous-Time and Discrete-Time Signals 151
3.1.3 Deterministic and Stochastic Systems 151
3.2 Properties of Systems 151
3.2.1 Causal and Noncausal Systems 151
3.2.2 Static (Memoryless) and Dynamic (with Memory) Systems . 152
3.2.3 Linear and Nonlinear Systems 155
3.2.4 Time-Invariant and Time-Variant Systems . 158
3.2.5 Invertible and Non-Invertible Systems . 165
3.2.5.1 Construction of the Inverse System 166
3.2.6 Stable and Unstable Systems 167
3.3 Solved Problems . 168
3.4 Homework Problems 176
4. Time Domain System Analysis 179
4.1 Impulse Response . 179
4.2 Continuous-Time Convolution 179
4.2.1 Computation of Convolution 180
4.2.2 The Command conv 186
4.2.3 Deconvolution 188
4.2.4 Continuous-Time Convolution Examples 189
4.3 Convolution Properties 199viii Contents
4.4 Interconnections of Systems . 202
4.5 Stability 206
4.6 Discrete-Time Convolution . 208
4.6.1 The Unit Impulse Sequence as Input to a System 208
4.6.2 Computation of Discrete-Time Convolution 211
4.6.3 Discrete-Time Convolution Examples . 219
4.7 Systems Described by Difference Equations 223
4.8 Filters 224
4.8.1 The Command filter . 224
4.8.2 Infinite Impulse Response Filters 228
4.8.3 Finite Impulse Response Filters . 232
4.9 Stability Criterion for Discrete-Time Systems 234
4.10 Systems Described by Differential Equations 235
4.11 Step Response of a System . 236
4.12 Solved Problems 237
4.13 Homework Problems . 245
5. Fourier Series 249
5.1 Orthogonality of Complex ExponentialSignals . 249
5.2 Complex Exponential Fourier Series 250
5.3 Trigonometric Fourier Series 253
5.4 Fourier Series in the Cosine with Phase Form 256
5.5 Plotting the Fourier Series Coefficients 258
5.6 Fourier Series of Complex Signals 263
5.7 Fourier Series of Periodic Signals . 265
5.8 Line Spectra . 270
5.9 Properties of Fourier Series . 272
5.9.1 Linearity . 272
5.9.2 Time Shifting 273
5.9.3 Time Reversal 275
5.9.4 Time Scaling . 275
5.9.5 Signal Multiplication . 276
5.10 Symmetry 277
5.10.1 Even Symmetry 277
5.10.2 Odd Symmetry 278
5.11 Parseval’s Identity . 280
5.12 Criterion for the Approximation of a Signal by a Fourier Series Expansion . 281
5.13 Relationship between Complex Exponential and Trigonometric
Fourier Series Coefficients 283
5.14 Solved Problems 285
5.15 Homework Problems . 297
6. Fourier Transform 301
6.1 Mathematical Definition 301
6.2 The Commands fourier and ifourier . 302
6.3 Fourier Transform Pairs 304
6.4 Properties of Fourier Transform . 305
6.5 Convolution in Time and Frequency . 311Contents ix
6.6 Symmetry of the Real and Imaginary Parts of Fourier Transform 312
6.7 Parseval’s Theorem . 313
6.8 Autocorrelation and Cross-Correlation 314
6.9 Solved Problems 318
6.10 Homework Problems 324
7. Fourier Analysis of Discrete-Time Signals . 327
7.1 Discrete-Time Fourier Transform . 327
7.2 Properties of Discrete-Time Fourier Transform . 329
7.3 Parseval’s Theorem for Discrete-Time Fourier Transform 336
7.4 Discrete Fourier Transform . 336
7.5 Properties of Discrete Fourier Transform 339
7.6 Inverse Discrete Fourier Transform 341
7.7 Circular Shift of a Sequence 342
7.7.1 Discrete Fourier Transform of a Circularly Shifted Sequence 346
7.8 Circular Convolution 347
7.8.1 Discrete Fourier Transform of Circular Convolution . 351
7.8.2 Relationship between Linear and Circular Convolution 352
7.9 Fast Fourier Transform 353
7.10 Relationship between DFT and DTFT . 357
7.11 Relationship between Fourier Transform andDiscrete Fourier Transform 360
7.12 Linear Convolution Computation via Fast Fourier Transform . 361
7.13 Solved Problems 362
7.14 Homework Problems 370
8. Frequency Response 373
8.1 Continuous-Time Frequency Response . 373
8.2 The Command freqs 376
8.2.1 The Command invfreqs 381
8.3 The Command lsim . 383
8.4 System Response to Sinusoidal Input 384
8.5 Ideal Filters 389
8.6 Frequency Response of Discrete-Time Systems . 394
8.7 The Command freqz 396
8.7.1 The Command invfreqz . 397
8.8 System Response to Discrete-Time SinusoidalInput 399
8.9 Moving Average Filter 399
8.10 Solved Problems 401
8.11 Homework Problems 411
9. Laplace Transform 415
9.1 Mathematical Definition 415
9.2 Commands laplace and ilaplace . 416
9.3 Region of Convergence . 419
9.4 Laplace Transform Pairs . 420
9.5 Laplace Transform Properties and Theorems 421
9.6 Partial Fraction Expansion of a Rational Function 425
9.6.1 The Command residue 429x Contents
9.7 Convolution in Time and in Complex Frequency . 432
9.7.1 Convolution in the Time Domain 432
9.7.2 Convolution in the Complex Frequency Domain 433
9.8 Using the Laplace Transform to Solve Differential Equations 433
9.9 Solved Problems 436
9.10 Homework Problems . 441
10. z-Transform 443
10.1 Mathematical Definition 443
10.2 Commands ztrans and iztrans . 444
10.3 Region of Convergence . 446
10.4 z-Transform Pairs 446
10.5 Properties of z-Transform . 447
10.6 Partial Fraction Expansion of a Rational Function . 453
10.6.1 Commands residue and residuez . 455
10.7 Using the z-Transform to Solve Difference Equations . 457
10.8 Solved Problems 460
10.9 Homework Problems . 467
11. Transfer Function 471
11.1 Continuous-Time Systems 471
11.2 The tf Command . 473
11.3 Stability of Continuous-Time Systems . 475
11.4 Transfer Function in Zero=Pole=Gain Form . 477
11.5 Interconnections of Systems . 478
11.6 Continuous-Time System Response . 481
11.7 Discrete-Time Systems . 485
11.8 The Command tf for Discrete-Time Systems . 486
11.9 Stability of Discrete-Time Systems . 486
11.10 Discrete-Time System Response . 489
11.10.1 Step Response . 489
11.10.2 Impulse Response . 491
11.10.3 The Command dlsim . 493
11.11 Conversion between Continuous-Time and Discrete-Time Systems . 494
11.12 Transfer Function and Frequency Response 495
11.13 Bode Plot 498
11.14 State-Space Representation 499
11.14.1 Construction of a State-Space Model . 503
11.14.2 Discrete-Time State-Space Models . 506
11.15 Solved Problems 508
11.16 Homework Problems 518
12. Suggested Laboratory Exercises 523
12.1 Laboratory 1: Introduction to MATLAB . 523
12.2 Laboratory 2: Signals . 524
12.3 Laboratory 3: Systems . 525
12.4 Laboratory 4: Time Domain System Analysis . 525
12.5 Laboratory 5: Fourier Series . 526
12.6 Laboratory 6: Fourier Transform 527Contents xi
12.7 Laboratory 7: Fourier Analysis of Discrete-Time Systems 528
12.8 Laboratory 8: Frequency Response 528
12.9 Laboratory 9: Laplace Transform 529
12.10 Laboratory 10: z-Transform 530
12.11 Laboratory 11: Transfer Function 531
Appendix A: Signal Crossword 533
Appendix B: Notation 535
Bibliography 537
Index 539
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