Index

algorithms, 24, 80, 171, 207, 398

adapted to sampling irregularities, 398, 405

comparison of, 130, 408

development of firmware for, 401

iterative, 292, 403, 407

performance of, 406, 408

sequential exclusion of components for, 401

spectrum analysis for, 292, 307, 401

aliasing, 3, 15, 158

compensation, 302

frequencies of, 76, 285

fuzzy, 185, 209

primary, 181

processes, 167

secondary, 181

spatial, 332–3

suppression of, 286

analog-digital conversion, 7–9

deterministic, 3

distributed, 151, 223–4

randomized, 3, 9

pseudo-randomized 3

analog-stochastic converter, 42

array of sensors

complexity reduction of, 419

directional pattern, 337–8, 344

randomized, 325

large aperture, 325, 419

model of, 326

nonuniform, 344

array signals, 328

analysis of, 330, 332

in spatial domain, 334

in temporal domain, 329

beamforming, 335

processing of, 419

adapted to sensor coordinates, 420

average parameters of signals

estimation of, 136

optimized estimation of

unbiased estimation of, 124

bias error, 124–5, 136

for randomised quantizing, 97

from aliasing

elimination of, 124

for deterministic quantizers, 124

correlation, 258

analysis, 201, 255, 264

coefficient

cross-correlation, 260

function, 255, 259

covariance

between a signal and quantization noise, 104, 119

cross-interference

adapting to, 356, 358

approximation of, 350

between signal components, 356

between spatial signals, 420

coefficients, 290–1, 347, 349, 356, 364, 406, 420–1

impact on DFT, 289, 349

taking into account of, 291, 353, 356

data acquisition, 139, 213, 227

fault tolerant, 416, 418

massive, 155, 221, 299

multichannel, 155, 221

spatial, 325

data compression

approach to, 391, 411

1D signals of, 392, 414

2D signals of, 415, 417

decomposed signal

nonuniformly sampled, 356

digital-stochastic converter, 43

discrete Fourier transform

approaches to, 284

basis functions of, 308

orthogonal exponential

orthogonal rectangular, 308

unorthogonal rectangular, 310–2, 315

complexity-reduced, 307, 318

display of, 166, 319

for signals sampled at sine-wave crossings, 322–4

for nonuniformly sampled signal, 177, 283, 308

for pseudo-randomly sampled signal, 289, 290

for spatial signals, 423

dither, 45, 243–4

embedded systems, 398

dedicated services of, 408

generic model of, 396

errors

from aliasing, 71

from quantizing, 97, 231, 252, 388–9

from randomized sampling, 251, 252, 284

in signal parameter estimates, 71, 73–4, 298

in spectral analysis, 284, 298

regularization of, 295, 298

estimate

Fourier coefficient of, 269, 298–9

mean absolute value of, 74, 243, 251

mean power of, 79, 227, 244, 252

mean value of a mono harmonic signal, 74, 350

signal parameter of, 227, 293

spectral, adapted to sampling non-uniformities, 356

estimation

absolute mean value of, 246

alias-free, 293

correlation functions of, 255, 261, 265

direction of arrival, 337, 339

errors, 247–8, 251, 284

mean power of, 249

object parameters of, 367

optimal, 234, 236, 239

signal parameters of, 233, 293, 298, 350

time intervals, 388

unbiased, 247

expected value

aliasing of, 288

average signal parameter of, 72, 123–4, 351

functionally converted signal of, 72, 137

multiplied quantized signals of, 256

pseudo-randomized quantizing error of, 117

pseudo-randomly quantized signal of, 109

randomly quantized signal of, 97–8

squared mean estimate of, 350

fast Fourier transforms, 80

exploitation of, 291–3, 295

nonuniformly sampled signals for, 209, 291, 293

filters

DFT based, 299, 300–1, 305, 317

frequency response of, 300, 305

selective, 304

functionally converted signal, 72, 136

estimation of, 72–5, 136–7

hybrid sampling, 80–3, 191, 206

double hybrid sampling, 81–2, 198, 207

input-expected output relationship, 44

input-output relationship

deterministic quantizing of, 44

pseudorandomized quantizing of, 115, 118

randomized quantizing of, 90

logic gate

stochastic computing for, 42

measurement

frequency response of, 367, 369

time intervals of, 386

model of quantizing, 94

moment of signal distribution, 122–3, 228

estimation of, 124, 228

Monte Carlo method, 34–5

instrumental implementation of, 36

noise

deterministic quantizing of, 118

pseudo-randomized quantizing of, 117–9, 121

randomized quantizing of, 118

regularization of, 297

spectra of, 121

number of samples, 231

for estimating average parameters, 231

minimizing of, 234, 248

Nyquist limit, 298

optimal estimation, 234

criterion, 234, 236–8

optimal quantizing, 109

for average parameter estimation, 109–112, 234

overlapping spectra, 69

signal components of, 15, 76

polarity coincidence method, 36–9

probabilistic encoding of signals, 41

probability density function

quantizing errors of, 98–101, 118

sampling intervals of, 128–9, 133, 351

signals of, 117, 250, 258

pseudo-randomized sampling, 82, 220

quantization, 7

deterministic, 87, 91, 118

error of, 97, 115

noise of, 97, 103, 117, 118

pseudo-randomized, 3, 107, 111–3, 118, 121, 232, 242, 255

randomized, 3, 87, 90, 118, 232

rough, 88, 109

step of, 87–8

quantized signal

processing of, 243–4

properties of, 92–7, 121

spectrum of, 105, 120

randomized digitizing, 127

sampling, 7

double hybrid, 80

function, 132–4

generalized model of, 65

irregularities, 284, 290, 356, 405

level-crossing of, 141

nonuniform, 80, 139, 192, 289, 356

periodic, 63, 65, 80, 192, 206

phase-shifted periodic, 158

point processes, 67, 128, 356

pseudo-randomized, 3, 80, 82, 172, 181

pulse trains, 171–2

randomized, 3, 63, 66, 80, 82, 127–8, 131, 139

remote, 150–1, 299

sine-wave crossings at, 294

theorem, 8, 80

threshold-crossing of, 140

sampling process

additive random, 66, 131, 182–3

additive pseudo-random, 203–4

decomposing of, 165, 183–5

nonuniform, 6, 16, 82, 165, 191

periodic, 6, 15, 66–7, 191, 204

with jitter, 65, 128, 184, 201

with random skips, 163–4, 179

sparse, 17

signal-to-noise ratio, 122, 408

signals

analog, 7

array, 328, 333

bio-impedance, 390–1

discrete-time, 7

multifrequency, 369

radio-frequency, 19, 411

quantized, 88, 118, 256

sampled, 15

periodically, 15

pseudo-randomly, 21, 264, 284–5

randomly, 16

sine-wave crossings at, 294

synthesis of, 371, 375, 379, 383

wideband, 382, 411

signal digitizing, 1, 4, 23–5

alias-free, 6, 12, 14

randomized, 4

pseudo-randomized, 10

signal processing

adapted to sampling nonuniformities, 347

adapted to sensor coordinates, 420–1

demodulation, 390, 392

fault tolerant, 416, 418–9

iterative, 403, 407, 418

one dimentional, 409, 418

two dimensional, 421, 424

signal transforms, 269

basis functions of, 271

orthogonal, 274

unorthogonal, 277

signal waveforms

reconstruction of, 160–2, 284, 409, 412

resampling, 409, 412

sine-wave crossings, 144–7, 151

spectra

periodically sampled signals of, 68–9, 307

quantized signals of, 105, 120

nonuniformly sampled signals of, 69, 70–1, 307

spatial, 328, 422–4

temporal, 328

spectrum analysis

adapting to sampling irregularities, 356

complexity-reduced, 307

spatial, 339, 340, 422–4

temporal, 277, 339, 340

statistical experimenting, 35

stochastic computing, 40–4

stochastic-ergodic conversion, 39, 40

variance

average parameter estimates of, 228

estimated mean values of, 125, 247

estimated mean power of, 250, 252

estimation errors of, 262, 389

quantization errors of, 98, 100, 117, 389

quantized signals of, 101–3, 111–2

signals of, 258