Signals and Systems using MATLAB

Front cover
......Page 1
Signals and Systems Using MATLAB®......Page 2
Copyright page......Page 3
Dedication......Page 4
Table of contents......Page 5
Preface......Page 12
Acknowledgments......Page 17
Part 1: Introduction
......Page 18
0.1 Signals and Systems and Digital Technologies......Page 20
0.2 Examples of Signal Processing Applications......Page 22
0.3 Analog or Discrete?......Page 26
0.4 Complex or Real?......Page 37
0.5 Soft Introduction to MATLAB......Page 46
Problems......Page 70
Part 2: Theory and Application of Continuous-Time Signals and Systems......Page 80
1.1 Introduction......Page 82
1.2 Classification of Time-Dependent Signals......Page 83
1.3 Continuous-Time Signals......Page 84
1.4 Representation Using Basic Signals......Page 102
1.5 What Have We Accomplished? Where Do We Go from Here?......Page 123
Problems......Page 125
2.1 Introduction......Page 134
2.2 System Concept......Page 135
2.3 LTI Continuous-Time Systems......Page 136
2.4 What Have We Accomplished? Where Do We Go from Here?......Page 173
Problems......Page 174
3.1 Introduction......Page 182
3.2 The Two-Sided Laplace Transform......Page 183
3.3 The One-Sided Laplace Transform......Page 193
3.4 Inverse Laplace Transform......Page 214
3.5 Analysis of LTI Systems......Page 231
Problems......Page 243
4.1 Introduction......Page 254
4.2 Eigenfunctions Revisited......Page 255
4.3 Complex Exponential Fourier Series......Page 262
4.4 Line Spectra......Page 265
4.5 Trigonometric Fourier Series......Page 268
4.6 Fourier Coefficients from Laplace......Page 272
4.7 Convergence of the Fourier Series......Page 282
4.8 Time and Frequency Shifting......Page 287
4.9 Response of LTI Systems to Periodic Signals......Page 290
4.10 Other Properties of the Fourier Series......Page 296
4.11 What Have We Accomplished? Where Do We Go from Here?......Page 306
Problems......Page 307
5.1 Introduction......Page 316
5.2 From the Fourier Series to the Fourier Transform......Page 317
5.4 Fourier Transforms from the Laplace Transform......Page 319
5.5 Linearity, Inverse Proportionality, and Duality......Page 321
5.6 Spectral Representation......Page 330
5.7 Convolution and Filtering......Page 344
5.8 Additional Properties......Page 361
Problems......Page 367
6.1 Introduction......Page 376
6.2 System Connections and Block Diagrams......Page 377
6.3 Application to Classic Control......Page 380
6.4 Application to Communications......Page 394
6.5 Analog Filtering......Page 407
Problems......Page 426
Part 3: Theory and Application of Discrete-Time Signals and Systems......Page 434
7.1 Introduction......Page 436
7.2 Uniform Sampling......Page 437
7.3 The Nyquist-Shannon Sampling Theorem......Page 454
7.4 Practical Aspects of Sampling......Page 456
7.5 What Have We Accomplished? Where Do We Go from Here?......Page 463
Problems......Page 464
8.1 Introduction......Page 468
8.2 Discrete-Time Signals......Page 469
8.3 Discrete-Time Systems......Page 495
Problems......Page 519
9.1 Introduction......Page 528
9.2 Laplace Transform of Sampled Signals......Page 529
9.3 Two-Sided Z-Transform......Page 532
9.4 One-Sided Z-Transform......Page 538
9.5 One-Sided Z-Transform Inverse......Page 559
Problems......Page 581
10.1 Introduction......Page 588
10.2 Discrete-Time Fourier Transform......Page 589
10.3 Fourier Series of Discrete-Time Periodic Signals......Page 613
10.4 Discrete Fourier Transform......Page 631
10.5 What Have We Accomplished? Where Do We Go from Here?......Page 645
Problems......Page 646
11.1 Introduction......Page 656
11.2 Frequency-Selective Discrete Filters......Page 658
11.3 Filter Specifications......Page 665
11.4 IIR Filter Design......Page 670
11.5 FIR Filter Design......Page 696
11.6 Realization of Discrete Filters......Page 706
Problems......Page 718
12.1 Introduction......Page 726
12.2 Application to Digital Signal Processing......Page 727
12.3 Application to Sampled-Data and Digital Control Systems......Page 739
12.4 Application to Digital Communications......Page 746
12.5 What Have We Accomplished? Where Do We Go from Here?......Page 758
Appendix. Useful Formulas......Page 760
Bibliography......Page 763
Index......Page 766