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| Percival D.B., Walden A.T. — Wavelet methods for time series analysis |
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| Предметный указатель |
Thresholding and SDF estimation, log periodogram and asymmetry 456
Thresholding and SDF estimation, log periodogram for AR(2) process 437—438
Thresholding and SDF estimation, log periodogram for AR(24) process 437—438
Thresholding and SDF estimation, log periodogram for MRC process 437—438
Thresholding and SDF estimation, log periodogram, RMSE 446
Thresholding, firm 400 411 453
Thresholding, global 399
Thresholding, hard 399 412 453
Thresholding, hard, level-dependent 445—449
Thresholding, hard, level-independent 445—446
Thresholding, hard, using D(4) partial DWT 418 420
Thresholding, hard, using LA(8) MODWT 430
Thresholding, hard, using LA(8) partial DWT 418—420 456
Thresholding, mid 399—400 453
Thresholding, mid and energy levels 420
Thresholding, mid, level-dependent 445—446
Thresholding, mid, level-independent 445—446
Thresholding, mid, using LA(8) MODWT 430
Thresholding, mid, using LA(8) partial DWT 419—420 456
Thresholding, paradigm 444 449 455
Thresholding, soft 399—340 422 453
Thresholding, soft and energy levels 420
Thresholding, soft, level-dependent 445—446
Thresholding, soft, level-independent 445—449
Thresholding, soft, using LA(8) MODWT 430
Thresholding, soft, using LA(8) partial DWT 419—421 423—424 456
Thresholding, wavelet 417 454
Tiao, G.C. 266 380—381 553 557
Time alignment 17 135 333 341 374 429
Time alignment and zero phase 182 203 234
Time alignment for boundary scaling and wavelet coefficients 137—138 146—147
Time alignment, LA and coiflet wavelet filters 136 155 188 193
Time invariant DWT 159
Time reversed filter, scaling 463 495
Time reversed filter, scaling, Fourier transform 465 484 496
Time reversed filter, scaling, key properties 499
Time reversed filter, scaling, squared gain function 485—486 498
Time reversed filter, wavelet 474 479 497
Time reversed filter, wavelet, Fourier transform 476 483 498
Time reversed filter, wavelet, key properties 499
Time series 1
Time series and its DWT 15
Time series, analysis (decomposition) 43 46 53 393
Time series, energy 42
Time series, reconstruction via DWT 16
Time series, sample ACS 14—15
Time series, synthesis (reconstruction) 43 46 53 393
Time series, vector form of 42
Time shift function, LA(L) wavelet filter of jth level 119 121
Time width of wavelet packet coefficients for node (j,n) 216
Time width, physical, for MODWPT of solar magnetic field 236
Time-dependent wavelet variance 296 324 333—334
Time-dependent wavelet variance, confidence intervals for 325
Time-independent wavelet variance 296 335
Time/frequency decomposition, DWPT 206
Time/frequency decomposition, matching pursuit 239
Time/frequency decomposition, MODWPT of solar magnetic field 236—237
Time/scale decomposition, DWT 206
Time/scale decomposition, matching pursuit 239
Toeplitz matrix 356 441
Top down basis selection 226
Torrence, C. 12 295 303 562
Torresani, B. 554
Toussoun, O. 191 562
Trace of a matrix 442
Trade-off between bias and variance 272
Transfer function (frequency response function) 25 33—34 267
Transfer function (frequency response function), Daubechies scaling filter 106
Transfer function (frequency response function), DWPT wavelet packet filter for node (j,n) 215 229 250
Transfer function (frequency response function), DWT scaling filter 76 78
Transfer function (frequency response function), DWT scaling filter of jth level 97 152 157
Transfer function (frequency response function), DWT wavelet filter 69
Transfer function (frequency response function), DWT wavelet filter of second level 91
Transfer function (frequency response function), DWT wavelet filter, jth level 96 152 157
Transfer function (frequency response function), filter with inserted zeros 91 96—97
Transfer function (frequency response function), high- and low-pass examples 26 39
Transfer function (frequency response function), MODWPT wavelet packet filter for node (j,n) 232
Transfer function (frequency response function), MODWT scaling and wavelet filters 163 469 476
Transfer function (frequency response function), MODWT scaling and wavelet filters of jth level 169 173 201 469 477
Transfer function (frequency response function), reversed filter 117
Transform coefficient 43
Transform, complex-valued see "Complex-valued transform"
Transform, discrete cosine see "Discrete cosine transform"
Transform, DWT see "Discrete wavelet transform"
Transform, isometric, 43 46—47 53
Transform, ODFT see "Orthonormal discrete Four transform"
Transform, orthonormal see "Orthonormal transform"
Transform, Walsh see "Walsh transform"
Transform, z 484 498
Transformation, variance stabilizing 270 275
Transformed RV, PDF of 258
Transformed RVs, joint PDF of 261
Transient 396
Translation 457—458 474 494
Translation by minus one unit 458
Translation by one unit 457
Translation invariant DWT 159
Translation invariant DWT, and MODWT 174
Translation, non-commuting with dilation 459
Transpose, complex conjugate (Hermitian) 45
Transpose, ordinary 42
Tree structure of DWT 451
Treitel, S. 488 561
Trend 317 319—320 323
Trend, estimation with LA(8), D(4) and C(6) filters 392
Trend, partial DWT applied to 368—369
Trend, plus FD process 368 383
Trend, plus FD process, estimation 383
Trend, plus FD process, filter length required 370
Trend, plus stationary process 289
Trend, test for 373 390
Trend, test for, and adjustment 373
Trend, test for, and mean removal 373
Trigamma function 275 376 391 440 442
Trigonometric polynomial 485
Tsai, C.-L. 424 557
Tsurutani, B.T. 552
Tsybakov, A. 556
Tukey, J.W. 51 255 269 297 317 553 562
Tukey, P.A. 554
Turbulence in the ocean 332 334
Two-fold cross-validation 402
Two-fold cross-validation, partial DWT 422
Two-fold cross-validation, threshold 423—424
Two-scale difference equation 465—466 495
Two-scale relationship 464 466 470 49
Two-sided exponential PDF 257
Two-stage cascade filter 304
Ulysses spacecraft 218 237
Ulysses spacecraft, solar polar orbit 219
Unbiased MODWT estimator of the wavelet variance 298 306 335 337
Uncorrelated Gaussian (normal) RVs 25
Uncorrelated Gaussian (normal) RVs and independence 259 407
Uncorrelated noise 393
Uncorrelated noise DWT coefficients 43 434
Uncorrelated non-Gaussian noise 417
Uncorrelated non-Gaussian wavelet coefficients 432
Undecimated DWT 159
Union of events 435
Unitary matrix 45—47 53
Unitary transform, energy preservation 46 53
Unitary transform, projection theorem 46
Universal threshold 400—401 418—419 443 450 453—454
Universal threshold, asymptotic considerations 401 439
Universal threshold, level-dependent 430
Universal thresholding, level-dependent 406 444—445 453 455
Universal thresholding, level-independent 444—445 455
Universal Time (UT) 219
Unser, M. 159 562
Upsampling 82—83 153 156 176—177 201
| UTC (Coordinated Universal Time) 317
Van Ness, J.W. 279—280 559
van Trees, H.L. 261 562
Vanishing discrete moments of time reversed wavelet filter 484 498
Vanishing moments 123 457
Vanishing moments of wavelet function 483—487 498
Vanishing moments, relationship to Fourier transform and derivatives of wavelet function 483—484
Variance mixture of Gaussian (normal) distribution 265 413
Variance of autoregressive process 294
Variance of chi-square RV 263 270
Variance of Gaussian (normal) RV 257
Variance of generalized Cauchy (t) RV 258
Variance of instantaneous LSE 392
Variance of Laplace (two-sided exponential) RV 257
Variance of log multitaper SDF estimator 275
Variance of log periodogram 270
Variance of periodogram 270
Variance of RV 256
Variance of sample mean 293
Variance of scaling coefficient 355
Variance of stationary stochastic process 266
Variance, inhomogeneity for Nile river minima 193
Variance, level-dependent for correlated noise DWT coefficients 441 456
Variance, stabilizing transformation 270 275
Variance, subtraction of two estimated values of 425 427
Variance, test for homogeneity of 341 379 391
Vector space basis for complex finite dimensional 46
Vector space basis for real finite dimensional 43—44 239
Vectors, complex-valued, inner product of 45
Vectors, complex-valued, squared norm of 46
Vectors, real-valued, inner product of 42
Vectors, real-valued, squared norm of 42
Vectors, transpose of 42
Veitch, D. 374 552
Venn diagram 473
Vertical ocean shear 193 295 327—328 330 396
Vertical ocean shear, bursts in MRA 194
Vertical ocean shear, MRA for LA(8) MODWT 193—195
Vertical ocean shear, NPESs 397
Vertical ocean shear, physical scales 194
Vertical ocean shear, representation via LA(8) DWT coefficients 397
Vertical ocean shear, representation via ODFT coefficients 397
Vertical ocean shear, wavelet variance estimates for 328—329 332—333
Vertical wind velocity average 6
Verveen, A.A. 340 561
Vessot, R.F.C. 553
Vetterli, M. 56 457 561—562
Vetterling, W.T. 560
Vial, P. 554
Vidakovic, B. 256 413—414 426—428 452 562
VisuShrink 420
von Steiger, R. 564
Wahba, G. 272 563
Walden, À.T. 217 239 247 272—274 303 340 355 379 411 417 442 559—561 563
Wallis, J.R. 191 559
Walsh transform 41
Walsh transform and Haar DWPT 217—218
Wang, G. 192 555
Wang, Y. 354 563
Watts, D.G. 269 317 557
Wavelet 2
Wavelet coefficients 13 17 59
Wavelet coefficients for AR(1) process 337
Wavelet coefficients, boundary elements, DWT 136 146 158 350
Wavelet coefficients, boundary elements, MODWT 198
Wavelet coefficients, compared to MODWT details of jth level 180 185
Wavelet coefficients, D(4) 60
Wavelet coefficients, decorrelation property 16 19 341
Wavelet coefficients, downsampling and bandwidth 85—86
Wavelet coefficients, downsampling and frequency reversal 85—86
Wavelet coefficients, finite energy function (signal) 479 497
Wavelet coefficients, IID Gaussian (normal) 417
Wavelet coefficients, jth level for finite energy function (signal) 480 497
Wavelet coefficients, mean of 301 335
Wavelet coefficients, nonboundary elements, correlation at different levels 346—347
Wavelet coefficients, nonboundary elements, covariance at different/same levels 345 348
Wavelet coefficients, nonboundary elements, SDF for 348—349 352
Wavelet coefficients, sample ACS 14 16 19 343
Wavelet coefficients, statistical properties 434
Wavelet coefficients, synthesis of finite energy function (signal) 482
Wavelet coefficients, time and scale 19
Wavelet coefficients, via circular filtering, DWT 70 74 80 88 92 94 152 157
Wavelet coefficients, via circular filtering, MODWPT 231 251
Wavelet coefficients, via circular filtering, MODWT 163 168—170 173 175 177 200—201
Wavelet correlation 303
Wavelet covariance 303
Wavelet details, DWT 64—65 151 158
Wavelet details, DWT, D(4) 65—66
Wavelet details, DWT, decomposition of sample variance 66—67
Wavelet details, DWT, first level 81
Wavelet details, DWT, Haar 64—65
Wavelet details, DWT, jth level, 95 191
Wavelet details, DWT, pseudo-code 102
Wavelet details, MODWT (jth level) 171 173 176—177 191 200 203
Wavelet details, MODWT (jth level) and DWT averaging 204—205
Wavelet details, MODWT (jth level), pseudo-code 179
Wavelet details, MODWT (jth level), via cross-correlation (circular) 172 203
Wavelet expansion, homogeneous 482
Wavelet expansion, inhomogeneous 482
Wavelet filter of jth level 95 152 343
Wavelet filter of jth level, advance required for C(L) 147 156
Wavelet filter of jth level, advance required for general design 118
Wavelet filter of jth level, advance required for LA(L) 146 155
Wavelet filter of jth level, alternative formulations 102
Wavelet filter of jth level, C(6) 125
Wavelet filter of jth level, connection to wavelet function 477 498
Wavelet filter of jth level, D(4) 97—98
Wavelet filter of jth level, Daubechies and band-pass nature 96 102
Wavelet filter of jth level, LA(8) 97—98
Wavelet filter of jth level, MODWT relationship to DWT 173
Wavelet filter of jth level, periodized 96—97
Wavelet filter of jth level, phase after advance for BL(L) 120
Wavelet filter of jth level, phase after advance for C(L) 124
Wavelet filter of jth level, phase after advance for LA(L) 114—115 120
Wavelet filter of jth level, shift factor for C(L) 124 198 205
Wavelet filter of jth level, shift factor for LA(8) 179
Wavelet filter of jth level, shift factor for LA(L) 114 198 20
Wavelet filter of jth level, squared gain function 157
Wavelet filter of jth level, time shift function for LA(L) 119 121
Wavelet filter of jth level, transfer function 96 152 157
Wavelet filter of jth level, width 96
Wavelet filter of second level 90—92
Wavelet filter of second level, Haar 40
Wavelet filter of second level, nonorthogonality to even shifts 92
Wavelet filter of second level, periodized 92
Wavelet filter of second level, transfer function 91
Wavelet filter, 'father' 80
Wavelet filter, advance required for LA(L) 113
Wavelet filter, approximately linear phase for LA(L) 112
Wavelet filter, autocorrelation 69
Wavelet filter, choice of 135 195
Wavelet filter, connection to wavelet function 477 498
Wavelet filter, construction of Daubechies type 457
Wavelet filter, D(4) 59 73 155
Wavelet filter, DWT 56 68 151 497
Wavelet filter, energy of 163
Wavelet filter, even width 68 74
Wavelet filter, extremal phase 61
Wavelet filter, Fourier transform of time reversed 476 483 498
Wavelet filter, Haar 60 73 75 155—156 192
Wavelet filter, key properties 154 202 499 500
Wavelet filter, lacking high-pass nature 105
Wavelet filter, least asymmetric see "LA(L)"
Wavelet filter, MODWT 163 168—169 200
Wavelet filter, MODWT, 'mother' 80
Wavelet filter, MODWT, applied circularly to finite sequence 296 336
Wavelet filter, MODWT, applied to infinite sequence 296 335
Wavelet filter, orthogonality to even shifted scaling filter 77 163
Wavelet filter, orthogonality to even shifts 69 71 151 163
Wavelet filter, orthonormality property 69
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