Structure and Interpretation of Signals and Systems

Signals and Systems......Page 31
Audio signals......Page 32
Images......Page 35
Video signals......Page 40
Signals representing physical attributes......Page 41
Sequences......Page 43
Discrete signals and sampling......Page 44
Systems as functions......Page 49
Telecommunications systems......Page 50
Audio storage and retrieval......Page 59
Modem negotiation......Page 60
Feedback control system......Page 61
Summary......Page 64
Declarative assignment......Page 67
Graphs......Page 69
Tables......Page 71
Composition......Page 72
Declarative vs. imperative......Page 77
Defining signals......Page 78
Imperative definitions......Page 79
Physical modeling......Page 80
Defining systems......Page 82
Differential equations......Page 83
Difference equations......Page 84
Composing systems using block diagrams......Page 86
State machines......Page 95
Stuttering......Page 97
State transition diagrams......Page 99
Update table......Page 104
State transition diagram......Page 108
Sets and functions model......Page 111
Simulation and bisimulation......Page 113
Relating behaviors......Page 118
Synchrony......Page 127
Side-by-side composition......Page 128
Cascade composition......Page 130
Product-form inputs and outputs......Page 133
General feedforward composition......Page 136
Hierarchical composition......Page 138
Feedback......Page 140
Feedback composition with no inputs......Page 141
Feedback composition with inputs......Page 146
Feedback composition of multiple machines......Page 148
Nondeterministic machines......Page 152
Operation of an infinite state machine......Page 157
Time......Page 159
One-dimensional SISO systems......Page 163
Zero-state and zero-input response......Page 166
Multidimensional SISO systems......Page 170
Multidimensional MIMO systems......Page 173
Continuous-time state-space models......Page 174
Frequency decomposition......Page 179
Phase......Page 185
Spatial frequency......Page 186
Periodic and finite signals......Page 187
Fourier series......Page 188
Periodic, finite, and aperiodic signals......Page 195
Discrete-time signals......Page 197
Periodicity......Page 198
The discrete-time Fourier series......Page 199
LTI systems......Page 205
Time invariance......Page 206
Linearity......Page 208
Linearity and time-invariance......Page 210
Discrete-time LTI systems......Page 212
Finding and using the frequency response......Page 213
The Fourier series with complex exponentials......Page 220
Negative frequencies......Page 221
Frequency response and the fourier series......Page 225
Cascade connection......Page 226
Feedback connection......Page 228
Filtering......Page 235
Convolution sum and integral......Page 236
Impulses......Page 241
Signals as sums of weighted delta functions......Page 242
Impulse response and convolution......Page 244
Frequency response and impulse response......Page 247
Finite impulse response (FIR) filters......Page 250
Design of FIR filters......Page 253
Decibels......Page 256
Designing IIR filters......Page 260
Implementation of filters......Page 262
Signal flow graphs......Page 264
Notation......Page 275
The Fourier series (FS)......Page 276
The discrete Fourier transform (DFT)......Page 277
The discrete-Time Fourier transform (DTFT)......Page 280
The continuous-time Fourier transform......Page 281
Conjugate symmetry......Page 284
Time shifting......Page 285
Linearity......Page 288
Constant signals......Page 289
Frequency shifting and modulation......Page 290
Sampling a sinusoid......Page 297
Aliasing......Page 298
Perceived pitch experiment......Page 300
Reconstruction......Page 303
A model for reconstruction......Page 305
The Nyquist-Shannon sampling theorem......Page 307
Sets......Page 315
Assignment and assertion......Page 316
Variables and predicates......Page 317
Quantification over sets......Page 319
Some useful sets......Page 320
Predicate operations......Page 321
Product sets......Page 323
Evaluating a predicate expression......Page 329
Functions......Page 332
Tuples and sequences as functions......Page 333
Function properties......Page 334
Summary......Page 337
Imaginary numbers......Page 341
Arithmetic of imaginary numbers......Page 342
Complex numbers......Page 343
Arithmetic of complex numbers......Page 344
Exponentials......Page 345
Polar coordinates......Page 346
Laboratory Exercises......Page 353
In-lab section......Page 356
Independent section......Page 359
Images in Matlab......Page 362
In-lab section......Page 364
Independent section......Page 366
Background......Page 370
In-lab section......Page 373
Independent section......Page 374
Background......Page 377
In-lab section......Page 379
Independent section......Page 380
In-lab section......Page 382
Independent section......Page 383
Background......Page 386
In-lab section......Page 388
Independent section......Page 389
Background......Page 393
In-lab section......Page 394
Independent section......Page 399
Background......Page 402
In-lab section......Page 405
Independent section......Page 406
Background......Page 408
In-lab section......Page 410
Independent section......Page 411
Background......Page 414
In-lab section......Page 419
Independent section......Page 421
In-lab section......Page 423