7/30/2019 3. Index.pdf

1/4

379

INDEX

Digital Signal Processing Using MATLABfor Students and Researchers, First Edition. John W. Leis. 2011 John Wiley & Sons, Inc. Published 2011 by John Wiley & Sons, Inc.

2s complement, 48

A/D converter, 45

aliasing, 8183, 231

analog filter conversion, 340

anti-aliasing filter, 82

arithmetic

fixed point, 52

floating point, 53

integer, 50

audio quantization, 67

autocorrelation, 165

average, 106

backprojection algorithm, 191

bandpass filter, 366

bilinear transform, 349

binary format, 34

binary multiplication, 51

binary representation, 47

bit allocation

audio & sound, 67

images, 67

SNR, 69

bitwise operators, 47

block diagram, 88

Butterworth filters, 326331

C programming language, 20

Chebyshev filters, 331339

color mixing, 77

color palette, 7879

complex Fourier series, 205

continuous Fourier transform, 212

convolution, 156159

definition, 158

example, 157

impulse response, 156

overlap-add, 310311

overlap-save, 311312

convolution via FFT, 364368

CORDIC, 56

correlation, 165

common signals, 171

noise removal, 204

cross-correlation, 168169

cumulative probability, 108109

D/A converter, 45

data files

binary, 3133

text, 3435

DCT

definition, 252

fast algorithm, 269

DCT. See discrete cosine transform

deterministic signals, 103

DFT. See discrete Fourier Transform

difference equation, 88

digital filters, 271

Direct Digital Synthesis (DDS), 131

discrete cosine transform, 252

discrete Fourier transform (DFT),

216231

compared to Fourier series, 218

component scaling, 219

examples, 220231

frequency scaling, 272

discrete-time filters, 271

discrete-time waveforms, 127

distributions

Gaussian, 112

generating, 120

ECG

filtering, 271

7/30/2019 3. Index.pdf

2/4

380 INDEX

fast convolution, 299

fast correlation, 301

fast Fourier transform (FFT), 244252

bit reversal, 252

complexity, 249derivation, 246

interpolation, 233

FFT see fast Fourier Transform

filter

bandpass, 283

bandstop, 283

highpass, 283

lowpass, 382

filter design, 274

direct method, 285frequency sampling method, 292

filter scaling, 362

filtering

overlap-add, 310311

overlap-save, 311312

filters

lowpass to bandpass, 366

lowpass to highpass, 364

phase linearity, 294

scaling, 362specification, 274

finite impulse response (FIR), 157

FIR. See finite impulse response

FIR filters, 285

direct design method, 285

frequency sampling design method,

292

FIR vs. IIR filters, 316

fixed point arithmetic, 52

floating point arithmetic, 53floating-point format, 53

Fourier series, 203209

derivation, 209210

phase shift, 211

Fourier series equations, 205

Fourier transform, 212

frequency response, 152

complex vector interpretation,

153155

MATLAB, 155156frequency scaling of filters, 362

gain/phase response, 273

Gaussian distribution, 112

grayscale, 4142

Hamming window, 289

heart waveform, 116

highpass filter, 283

histogram, 114115

histogram equalization, 118120histogram operators, 117

IIR. See infinite impulse response

IIR filters, 316

image display, 74

image quantization, 6769

image scanning, 75

impulse response, 88

impulse-invariant transform, 340348

infinite impulse response (IIR), 158159integer arithmetic, 50

interpolation, 8788, 233236

joint probability, 117

JPEG images, reading, 42

Lagrange polynomial, 8788

Laplacian distribution, 113

linear prediction, 177

linear time-invariant model, 9295linearity, 92

lookup table

waveform samples, 130131

lookup table, palette, 7879

MATLAB

arguments to functions, 26

audio reading, 35

calling a function, 26

function arguments, 26function example, 2829

function return values, 26

functions, 26

image reading, 35

m-files, 20

matrix/vector dimensions, 23

multidimensional arrays, 35

obtaining, 3, 19

path, 25

search path, 26startup file, 26

MATLAB code

aspect ratio, 41, 42

audio playback, 42

correlation, 169170

7/30/2019 3. Index.pdf

3/4

INDEX 381

cumulative probability, 108109

difference equation using filter, 92

difference equation: pole locations,

147

difference equation: sampled exponentialsignal, 140

difference equations, 8892

direct DFT computation, 219

direct DFT computation using vectorized

loop, 220

discrete frequency response,

155156

FFT interpolation, 233

filter function & difference equations,

144FIR direct method, 287

FIR window method, 291

first-order difference equation, 89

Fourier series, 209

Fourier series & phase shift,

211212

grayscale image display, 41

grayscale image example, 7980

Hamming window, 290

pole-zero plot, 149probability density, 110

pseudo-random numbers, 106

random image display, 41

random number generation, 41

random number realizations, 106

sampled exponential signal, 140

stair plots, 63

stem plots, 63

waveform via direct calculation, 130

MATLAB functionaddpath, 26

axis, 31, 41

bitand, 38

cat, 3537

clear all, 20

close all, 20

colormap, 42

conj, 148

fft, 220

fgetl, 32filter, 92, 144

fopen, 32

fprintf, 29

fread, 34

fscanf, 32

fwrite, 35

hist, 116

ifft, 230

image, 41

imread, 42legend, 30

load, 31

plot, 30

poly, 148

reshape, 234

residue, 346

roots, 148

save, 31

sort, 29

sound, 40, 137stairs, 63

stem, 63

wavread, 35

zeros, 39

MATLAB function help, 20

MATLAB function lookfor, 29

MATLAB operator

for, 24

if, 24

while, 24mean, 106

arithmetic, 107

population, 107

sample, 107

mean square, 107

median, 107

median filter, 122

mode, 107

multidimensional arrays, 35

noise cancellation, 184

notch filter, 278

numerical precision, 52

optimal filter, 183

overlap-add algorithm, 310311

overlap-save algorithm, 311312

palette, 7879

Parsevals Theorem, 268PDF, 109

periodic function, 204

poles of a system, 146

probability density function, 109

pseudo-random, 106

7/30/2019 3. Index.pdf

4/4

382 INDEX

quantization, 64

audio, 7071

image, 6869

SNR, 6974

quantizer characteristic, 64

Radon transform, 189

random signals, 103

random variable generation, 120

reconstruction, 62, 293

reconstruction filter, 62

recursive filters, 315

sample buffers, 241

sampling, 46, 61sampling impulses, 62

sampling terminology, 129

sampling windows, 236

Shepp-Logan head phantom, 12

Shepp-Logan phantom, 188

signal model, 105

signal processing

algorithm, 1

applications, 3

case studies, 4definition, 1

real-time, 2

signal-to-noise ratio, 69

sinc function, 86, 293294

stability, 146

sunspot observations, 204

superposition, 92

system identification, 175

time-frequency distributions, 240

time-invariance, 92tomography, 188

definition, 11

transfer function, 139

twos complement, 48

uniform distribution, 111

uniform PDF, 111

variance, 108

waveform generation

z transform, 137

direct calculation, 128

double buffering, 137

lookup table, 130

phase correction, 133

recurrence relation, 131

Wiener filter, 184

window function

Hamming, 2243, 289Hanning, 243

triangular, 242

z delay operator, 138

z transform examples, 140144

zero-order hold, 6162