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| Percival D.B., Walden A.T. — Wavelet methods for time series analysis |
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| Предметный указатель |
Wavelet filter, periodized 71 74 77 80 88 153 168—170 201
Wavelet filter, squared gain function 69 74 151 163
Wavelet filter, sum of zero 69 74 151 163
Wavelet filter, support of wavelet function 474
Wavelet filter, time reversed 474 479 497
Wavelet filter, transfer function 69 163 169 173 201 476—477
Wavelet filter, unit energy 69 71 74
Wavelet filter, vanishing discrete moments of time reversed 484 498
Wavelet filter, width 61 135 169 201
Wavelet filter, width and band-pass properties 315
Wavelet filter, width and mean of wavelet coefficients 3
Wavelet frames 159
Wavelet function 457 472 496—497
Wavelet function, as a small wave 2 476
Wavelet function, complex-valued 4
Wavelet function, computation for D(4) 477
Wavelet function, connection to MODWT wavelet filter of jth level 477 498
Wavelet function, finite support 474 498
Wavelet function, first derivative of Gaussian 3 10
Wavelet function, Fourier transform of 476 498
Wavelet function, Haar 475 479
Wavelet function, Haar, alternative formulation 2—3 9
Wavelet function, integral of zero 476 498
Wavelet function, integration of 2
Wavelet function, integration of square of 2
Wavelet function, key properties 499—500
Wavelet function, Mexican hat 3 10
Wavelet function, moments 483
Wavelet packet coefficients for node (j,n), time width 216
Wavelet packet coefficients for node (j,n), via circular filtering, 214—215 249—250
Wavelet packet coefficients, natural ordering 209—210
Wavelet packet coefficients, sequential frequency (sequency) ordering 209—210 212 232
Wavelet packet coefficients, via circular filtering 210 212 232
Wavelet packet cost table 225
Wavelet packet details (MODWPT), LA(8) for solar magnetic field 237—238
Wavelet packet details (MODWPT), node (j,n) via cross-correlation (circular) 234 251
Wavelet packet filter for node (j,n) 211 231 250—251
Wavelet packet filter for node (j,n), advance required for general design 231
Wavelet packet filter for node (j,n), advance required for LA(L) and C(L) 230 233 253
Wavelet packet filter for node (j,n), LA(8) 253
Wavelet packet filter for node (j,n), LA(L) and C(L) phase function 229
Wavelet packet filter for node (j,n), nominal pass-band 209 216—218 249
Wavelet packet filter for node (j,n), phase function 253
Wavelet packet filter for node (j,n), shift factor for LA(L) and C(L) 221 230
Wavelet packet filter for node (j,n), squared gain function 215 217 233 253
Wavelet packet filter for node (j,n), transfer function 215 229 232 250
Wavelet packet filter for node (j,n), width 214
Wavelet packet table (WP table) 209 212 250
Wavelet packet table (WP table), arbitrary disjoint dyadic decomposition of 213
Wavelet packet table (WP table), best basis 223 226 251
Wavelet packet table (WP table), best basis, algorithm 225
Wavelet packet table (WP table), best basis, example 224
Wavelet packet table (WP table), best shift basis 228
Wavelet packet table (WP table), disjoint dyadic decomposition, ANOVA 214
Wavelet packet table (WP table), disjoint dyadic decomposition, energy decomposition 214
Wavelet packet table (WP table), maximal overlap 232 251
Wavelet packet table (WP table), optimal transform 223 251
Wavelet packet table (WP table), optimal transform, example 224
Wavelet packet table (WP table), partial DWT as disjoint dyadic decomposition of 212
Wavelet packet table (WP table), vectors for waveform dictionary 241 254
Wavelet packet tree see "Wavelet packet table"
Wavelet roughs 66
Wavelet roughs, D(4) 65—66
Wavelet roughs, Haar 64 66
Wavelet shrinkage see "Shrinkage"
Wavelet smooths, DWT 64 66 151 158
Wavelet smooths, DWT, artifact removal by averaging 197
Wavelet smooths, DWT, D(4) 65—66
Wavelet smooths, DWT, first level 81
Wavelet smooths, DWT, Haar 64 66
Wavelet smooths, DWT, jth level 95
Wavelet smooths, DWT, pseudo-code 102
Wavelet smooths, MODWT and DWT averaging 204—205
Wavelet smooths, MODWT via cross-correlation (circular) 172 203
Wavelet smooths, MODWT, jth level 171 173 176—177 200 203
Wavelet smooths, MODWT, pseudo-code 179
| Wavelet spectrum 295
Wavelet thresholding see "Thresholding"
Wavelet variance 15 17 295
Wavelet variance and Allan variance 322
Wavelet variance and SDF 296—297 315—316 329 337 343
Wavelet variance for FD process 375
Wavelet variance for processes with stationary backward differences 305
Wavelet variance for random walk process 337
Wavelet variance for stationary processes 305
Wavelet variance for white noise process 337
Wavelet variance, confidence intervals for 311 313—314 319—320 327 332—334 336 345 385
Wavelet variance, estimates for atomic clock data 317 322 319—320 322—323
Wavelet variance, estimates for Nile River minima 327
Wavelet variance, estimates for vertical ocean shear 328—329 332
Wavelet variance, estimators, asymptotic properties of 295 307 311 336
Wavelet variance, estimators, based on Haar, D(4), D(6) and LA(8) filters 320 323 328—329
Wavelet variance, estimators, biased 307 308 337 351 378
Wavelet variance, estimators, leakage in 303
Wavelet variance, estimators, unbiased 298 306 308 335 337 375 384 390
Wavelet variance, exponents and stationary/nonstationary processes 323
Wavelet variance, scale-by-scale ANOVA 296 335
Wavelet variance, scale-by-scale ANOVA, proof of 301
Wavelet variance, time-dependent 296 324 333—334
Wavelet variance, time-independent 296 335
Wavelet, choice of 56
Wavelet-based analysis of covariance 303
Wavelet-based analysis of variance 19 296 335
Wavelet-based analysis of variance, proof of 301
Waveshrink 417
Weak differentiability 403—404 456
weighted averages 11
Weighted averages, changes in 162
Weighted least squares estimator (WLSE) for FD process 374 376 391
Weighted least squares estimator (WLSE) for FD process, MODWT-based 377—379 385
Weighted least squares estimator (WLSE) of atomic clock data 385
Weighted overlapped segment averaging (WOSA) spectral estimator 315
Weiss, J. 159 174 228 555
Welch, P.D. 315 563
Wells, R.O. 558
Whitcher 303 351 353 380 382 387 391 563
White noise 268 286 288 293—294 442
White noise, ACVS of 268
White noise, Gaussian (normal) 358 389
White noise, spectral density function of 268
White noise, wavelet variance for 337
Wickerhauser, M.V. 118 209 223 225 231 554 556 563
Width of equivalent filter for filter cascade 28
Width of filter 28 39 90
Width of scaling filter 75 78
Width of scaling filter, of jth level 97 169 201
Width of wavelet filter 61 68 74 135
Width of wavelet packet filter for node (j,n) 214
Width, time see "Time width"
Winkler, G.M.R. 553
Winterhalter, D. 564
WLSE see "Weighted least squares"
Wood, A.T.A. 290 563
Worneil, G.W. 295 340 355 361 366 563
WOSA spectral estimator 315
WP table see "Wavelet packet table"
Yaglom, A.M. 287 563
Yamanaka, M.D. 561
Yip, P. 54 560
Young, P.C. 560
Z transform of time reversed scaling filter 484 498
Zero padding 308 338 382 387
Zero phase filter 108 110 158 179 184
Zero phase filter and time alignment 182 203 234 237 252
Zero phase filter for MODWPT details for node (j,n) 234 252
Zero phase filter for MODWT details 189
Zero phase filter for MODWT details of jth level 172 168
Zero phase filter for MODWT smooths 168
Zero phase filter for MODWT smooths of jth level 172
Zhang, D. 557
Zhang, Z. 239—240 555 559
Zurbuchen, Th. 220 564
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