Fundamentals of signals and systems : a building block approach

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This innovative textbook provides a solid foundation in both signal processing and systems modeling using a building block approach. The authors show how to construct signals from fundamental building blocks (or basis functions), and demonstrate a range of powerful design and simulation techniques in Matlab, recognizing that signal data are usually received in discrete samples, regardless of whether the underlying system is discrete or continuous in nature. The book begins with key concepts such as the orthogonality principle and the discrete Fourier transform. Using the building block approach as a unifying principle, the modeling, analysis and design of electrical and mechanical systems are then covered, using various real-world examples. The design of finite impulse response filters is also described in detail. Containing many worked examples, homework exercises, and a range of Matlab laboratory exercises, this is an ideal textbook for undergraduate students of engineering, computer science, physics, and other disciplines.

Author Notes

Philip D. Cha is a professor in the Department of Engineering at Harvey Mudd College in Claremont, California
John I. Molinder is a professor in the Department of Engineering at Harvey Mudd College in Claremont, California

List of figures	p. x
List of tables	p. xxi
Preface	p. xxiii
Acknowledgments	p. xxvii
1 Introduction to signals and systems	p. 1
1.1 Signals and systems	p. 1
1.2 Examples of signals	p. 4
1.3 Mathematical foundations	p. 7
1.4 Phasors	p. 9
1.5 Time-varying frequency and instantaneous frequency	p. 12
1.6 Transformations	p. 14
1.7 Discrete-time signals	p. 18
1.8 Sampling	p. 22
1.9 Downsampling and upsampling	p. 23
1.10 Problems	p. 24
2 Constructing signals from building blocks	p. 29
2.1 Basic building blocks	p. 29
2.2 The orthogonality principle	p. 33
2.3 Orthogonal basis functions	p. 35
2.4 Fourier series	p. 42
2.5 Alternative forms of the Fourier series	p. 43
2.6 Approximating signals numerically	p. 47
2.7 The spectrum of a signal	p. 49
2.8 The discrete Fourier transform	p. 56
2.9 Variations on the DFT and IDFT	p. 59
2.10 Relationship between X[k] and C[subscript k]	p. 60
2.11 Examples	p. 62
2.12 Proof of the continuous-time orthogonality principle	p. 69
2.13 A note on vector spaces	p. 72
2.14 Problems	p. 78
3 Sampling and data acquisition	p. 85
3.1 Sampling theorem	p. 87
3.2 Discrete-time spectra	p. 88
3.3 Aliasing, folding and reconstruction	p. 89
3.4 Continuous- and discrete-time spectra	p. 96
3.5 Aliasing and folding (time domain perspective)	p. 97
3.6 Windowing	p. 104
3.7 Aliasing and folding (frequency domain perspective)	p. 106
3.8 Handling data with the FFT	p. 110
3.9 Problems	p. 112
4 Lumped element modeling of mechanical systems	p. 118
4.1 Introduction	p. 118
4.2 Building blocks for lumped mechanical systems	p. 121
4.3 Inputs to mechanical systems	p. 131
4.4 Governing equations	p. 132
4.5 Parallel combination	p. 141
4.6 Series combination	p. 144
4.7 Combination of masses	p. 146
4.8 Examples of parallel and series combinations	p. 146
4.9 Division of force in parallel combination	p. 147
4.10 Division of displacement in series combination	p. 148
4.11 Problems	p. 150
5 Lumped element modeling of electrical systems	p. 158
5.1 Building blocks for lumped electrical systems	p. 158
5.2 Summary	p. 165
5.3 Inputs to electrical systems	p. 166
5.4 Governing equations	p. 167
5.5 Parallel combination	p. 172
5.6 Series combination	p. 175
5.7 Division of current in parallel combination	p. 177
5.8 Division of voltage in series combination	p. 177
5.9 Problems	p. 178
6 Solution to differential equations	p. 183
6.1 First-order ordinary differential equations	p. 184
6.2 Second-order ordinary differential equations	p. 185
6.3 Transient response	p. 189
6.4 Transient specifications	p. 196
6.5 State space formulation	p. 199
6.6 Problems	p. 211
7 Input-output relationship using frequency response	p. 217
7.1 Frequency response of linear, time-invariant systems	p. 219
7.2 Frequency response to a periodic input and any arbitrary input	p. 221
7.3 Bode plots	p. 222
7.4 Impedance	p. 238
7.5 Combination and division rules using impedance	p. 241
7.6 Problems	p. 249
8 Digital signal processing	p. 266
8.1 More frequency response	p. 268
8.2 Notation clarification	p. 270
8.3 Utilities	p. 271
8.4 DSP example and discrete-time FRF	p. 272
8.5 Frequency response of discrete-time systems	p. 281
8.6 Relating continuous-time and discrete-time frequency response	p. 291
8.7 Finite impulse response filters	p. 299
8.8 The mixer	p. 305
8.9 Problems	p. 307
9 Applications	p. 310
9.1 Communication systems	p. 310
9.2 Modulation	p. 310
9.3 AM radio	p. 311
9.4 Vibration measuring instruments	p. 317
9.5 Undamped vibration absorbers	p. 323
9.6 JPEG compression	p. 325
9.7 Problems	p. 335
10 Summary	p. 341
10.1 Continuous-time signals	p. 343
10.2 Discrete-time signals	p. 345
10.3 Lumped element modeling of mechanical and electrical systems	p. 347
10.4 Transient response	p. 350
10.5 Frequency response	p. 351
10.6 Impedance	p. 353
10.7 Digital signal processing	p. 354
10.8 Transition to more advanced texts (or, what's next?)	p. 356
Laboratory exercises	p. 363
Laboratory exercise 1 Introduction to MATLAB	p. 365
L1.1 Objective	p. 365
L1.2 Guided introduction to MATLAB	p. 365
L1.3 Vector and matrix manipulation	p. 366
L1.4 Variables	p. 370
L1.5 Plotting	p. 371
L1.6 M-files	p. 373
L1.7 Housekeeping	p. 377
L1.8 Summary of MATLAB commands	p. 378
L1.9 Exercises	p. 379
Laboratory exercise 2 Synthesize music	p. 382
L2.1 Objective	p. 382
L2.2 Playing sinusoids	p. 382
L2.3 Generating musical notes	p. 383
L2.4 Fur Elise project	p. 385
L2.5 Extra credit	p. 386
L2.6 Exercises	p. 387
Laboratory exercise 3 DFT and IDFT	p. 388
L3.1 Objective	p. 388
L3.2 The discrete Fourier transform	p. 388
L3.3 The inverse discrete Fourier transform	p. 391
L3.4 The fast Fourier transform	p. 392
L3.5 Exercises	p. 393
Laboratory exercise 4 FFT and IFFT	p. 394
L4.1 Objective	p. 394
L4.2 Frequency response of a parallel RLC circuit	p. 395
L4.3 Time response of a parallel RLC circuit to a sweep input	p. 396
L4.4 Exercises	p. 399
Laboratory exercise 5 Frequency response	p. 400
L5.1 Objective	p. 400
L5.2 Automobile suspension	p. 400
L5.3 Frequency response	p. 400
L5.4 Time response to sinusoidal input	p. 401
L5.5 Numerical solution with the Fourier transform	p. 402
L5.6 Time response to step input	p. 403
L5.7 Optimizing the suspension	p. 404
L5.8 Exercises	p. 404
Laboratory exercise 6 DTMF	p. 405
L6.1 Objective	p. 405
L6.2 DTMF dialing	p. 405
L6.3 fdomain and tdomain	p. 406
L6.4 Band-pass filters	p. 407
L6.5 DTMF decoding	p. 407
L6.6 Forensic engineering	p. 408
L6.7 Exercises	p. 408
Laboratory exercise 7 AM radio	p. 409
L7.1 Objective	p. 409
L7.2 Amplitude modulation	p. 409
L7.3 Demodulation	p. 410
L7.4 Pirate radio	p. 411
L7.5 Exercises p. 412
Appendix A Complex arithmetic	p. 413
Appendix B Constructing discrete-time signals from building blocks - least squares	p. 416
Appendix C Discrete-time upsampling, sampling and downsampling	p. 419
Index	p. 425

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Table of Contents