The Scientist and Engineer's Guide to Digital Signal Processing

Table of Contents......Page 5
FOUNDATIONS:......Page 6
The Roots of DSP......Page 15
Compression......Page 18
Music......Page 19
Speech recognition......Page 20
Radar......Page 21
Reflection seismology......Page 22
Medical......Page 23
Commercial Imaging Products......Page 24
Signal and Graph Terminology......Page 25
Mean and Standard Deviation......Page 27
Signal vs. Underlying Process......Page 31
The Histogram, Pmf and Pdf......Page 33
The Normal Distribution......Page 40
Digital Noise Generation......Page 43
Precision and Accuracy......Page 46
Quantization......Page 49
The Sampling Theorem......Page 53
Digital-to-Analog Conversion......Page 58
Analog Filters for Data Conversion......Page 62
Selecting The Antialias Filter......Page 69
Multirate Data Conversion......Page 72
Single Bit Data Conversion......Page 74
Computer Numbers......Page 81
Fixed Point (Integers)......Page 82
Floating Point (Real Numbers)......Page 84
Number Precision......Page 86
Execution Speed: Program Language......Page 90
Execution Speed: Hardware......Page 94
Execution Speed: Programming Tips......Page 99
FUNDAMENTALS:......Page 7
Signals and Systems......Page 101
Requirements for Linearity......Page 103
Static Linearity and Sinusoidal Fidelity......Page 106
Examples of Linear and Nonlinear Systems......Page 108
Examples of Nonlinear Systems......Page 109
Special Properties of Linearity......Page 110
Superposition: the Foundation of DSP......Page 112
Step Decomposition......Page 114
Even/Odd Decomposition......Page 116
Interlaced Decomposition......Page 117
Alternatives to Linearity......Page 118
The Delta Function and Impulse Response......Page 121
Convolution......Page 122
The Input Side Algorithm......Page 126
The Output Side Algorithm......Page 130
The Sum of Weighted Inputs......Page 136
Delta Function......Page 137
Calculus-like Operations......Page 139
Low-pass and High-pass Filters......Page 142
Causal and Noncausal Signals......Page 144
Amplitude Amplitude......Page 145
Commutative Property......Page 146
Associative Property......Page 147
Transference between the Input and Output......Page 148
The Central Limit Theorem......Page 149
Correlation......Page 150
Speed......Page 154
The Family of Fourier Transform......Page 155
Periodic-Discrete......Page 158
Notation and Format of the Real DFT......Page 160
The Frequency Domain's Independent Variable......Page 162
DFT Basis Functions......Page 164
Synthesis, Calculating the Inverse DFT......Page 166
DFT by Correlation......Page 171
Polar Notation......Page 175
Nuisance 1: Radians vs. Degrees......Page 178
Nuisance 3: Incorrect arctan......Page 179
Nuisance 5: 2B B ambiguity of the phase......Page 180
Nuisance 6: The magnitude is always positive......Page 181
Nuisance 7: Spikes between Pi and -Pi......Page 182
Spectral Analysis of Signals......Page 183
Frequency Response of Systems......Page 191
Convolution via the Frequency Domain......Page 194
Linearity of the Fourier Transform......Page 199
Characteristics of the Phase......Page 202
Periodic Nature of the DFT......Page 208
Compression and Expansion, Multirate methods......Page 214
Multiplying Signals......Page 218
The Discrete Time Fourier Transform......Page 220
Parseval's Relation......Page 222
Delta Function Pairs......Page 223
The Sinc Function......Page 226
Other Transform Pairs......Page 229
Gibbs Effect......Page 232
Harmonics......Page 234
Chirp Signals......Page 236
Real DFT Using the Complex DFT......Page 239
How the FFT works......Page 242
FFT Programs......Page 247
Speed and Precision Comparisons......Page 251
Further Speed Increases......Page 252
The Delta Function......Page 257
Convolution......Page 260
The Fourier Transform......Page 266
The Fourier Series......Page 269
DIGITAL FILTERS:......Page 8
Filter Basics......Page 275
How Information is Represented in Signals......Page 279
Time Domain Parameters......Page 280
Frequency Domain Parameters......Page 282
High-Pass, Band-Pass and Band-Reject Filters......Page 285
Filter Classification......Page 288
Implementation by Convolution......Page 291
Noise Reduction vs. Step Response......Page 292
Relatives of the Moving Average Filter......Page 294
Recursive Implementation......Page 296
Strategy of the Windowed-Sinc......Page 299
Designing the Filter......Page 302
Examples of Windowed-Sinc Filters......Page 306
Pushing it to the Limit......Page 307
Arbitrary Frequency Response......Page 311
Deconvolution......Page 314
Optimal Filters......Page 321
The Overlap-Add Method......Page 325
FFT Convolution......Page 326
Speed Improvements......Page 330
The Recursive Method......Page 333
Single Pole Recursive Filters......Page 336
Narrow-band Filters......Page 340
Phase Response......Page 342
Using Integers......Page 346
The Chebyshev and Butterworth Responses......Page 347
Designing the Filter......Page 348
Step Response Overshoot......Page 352
Stability......Page 353
Match #1: Analog vs. Digital Filters......Page 357
Match #2: Windowed-Sinc vs. Chebyshev......Page 360
Match #3: Moving Average vs. Single Pole......Page 362
APPLICATIONS:......Page 9
Human Hearing......Page 365
Timbre......Page 369
Sound Quality vs. Data Rate......Page 372
High Fidelity Audio......Page 373
Companding......Page 376
Speech Synthesis and Recognition......Page 378
Nonlinear Audio Processing......Page 382
Digital Image Structure......Page 387
Cameras and Eyes......Page 390
Television Video Signals......Page 398
Other Image Acquisition and Display......Page 400
Brightness and Contrast Adjustments......Page 401
Grayscale Transforms......Page 404
Warping......Page 408
Convolution......Page 411
3×3 Edge Modification......Page 416
Convolution by Separability......Page 418
Example of a Large PSF: Illumination Flattening......Page 421
Fourier Image Analysis......Page 424
FFT Convolution......Page 430
A Closer Look at Image Convolution......Page 432
Spatial Resolution......Page 437
Sample Spacing and Sampling Aperture......Page 444
Signal-to-Noise Ratio......Page 446
Morphological Image Processing......Page 450
Computed Tomography......Page 456
Target Detection......Page 465
Neural Network Architecture......Page 472
Why Does It Work?......Page 477
Training the Neural Network......Page 479
Evaluating the Results......Page 487
Recursive Filter Design......Page 490
Data Compression Strategies......Page 495
Run-Length Encoding......Page 497
Huffman Encoding......Page 498
Delta Encoding......Page 500
LZW Compression......Page 502
JPEG (Transform Compression)......Page 508
MPEG......Page 515
How DSPs are Different from Other Microprocessors......Page 517
Circular Buffering......Page 520
Architecture of the Digital Signal Processor......Page 523
Fixed versus Floating Point......Page 528
C versus Assembly......Page 534
How Fast are DSPs?......Page 540
Digital Signal Processor Market......Page 545
29 Gettings Started with DSPs......Page 549
COMPLEX TECHNIQUES:......Page 11
The Complex Number System......Page 565
Using Complex Numbers by Substitution......Page 571
Complex Representation of Sinusoids......Page 573
Complex Representation of Systems......Page 575
Electrical Circuit Analysis......Page 577
The Real DFT......Page 581
Mathematical Equivalence......Page 583
The Complex DFT......Page 584
2. Real versus Complex......Page 589
7. The Synthesis Equations......Page 590
Why the Complex Fourier Transform is Used......Page 591
The Nature of the s-Domain......Page 595
Strategy of the Laplace Transform......Page 602
Analysis of Electric Circuits......Page 606
The Importance of Poles and Zeros......Page 611
Filter Design in the s-Domain......Page 614
The Nature of the z-Domain......Page 619
Analysis of Recursive Systems......Page 624
Cascade and Parallel Stages......Page 630
Spectral Inversion......Page 633
Gain Changes......Page 635
Combining Coefficients......Page 637
Warp from Circle to Ellipse......Page 638
Continuous to Discrete Conversion......Page 640
Low-pass to Low-pass Frequency Change......Page 642
Low-pass to High-pass Frequency Change......Page 643
The Best and Worst of DSP......Page 644
B......Page 645
C......Page 646
D......Page 647
E......Page 648
F......Page 649
H......Page 650
L......Page 651
P......Page 652
R......Page 653
S......Page 654
Z......Page 656
C......Page 657
D......Page 658
F......Page 659
M......Page 661
P......Page 662
S......Page 663
Z......Page 664