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Summary
Summary
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
Table of Contents
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 |