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| Авторизация |
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| Percival D.B., Walden A.T. — Wavelet methods for time series analysis |
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| Предметный указатель |
Purely random process 268
Pyramid algorithm for DWT 17 56 68 151 157
Pyramid algorithm for DWT, first stage 80
Pyramid algorithm for DWT, first stage, and DWPT 207
Pyramid algorithm for DWT, first stage, summary 86
Pyramid algorithm for DWT, general stage 93
Pyramid algorithm for DWT, general stage, summary 99
Pyramid algorithm for DWT, inverse 95 157
Pyramid algorithm for DWT, pseudo-code 100 157
Pyramid algorithm for DWT, pseudo-code for inverse 101 157
Pyramid algorithm for DWT, reformulation for general length series 144
Pyramid algorithm for DWT, second stage 88
Pyramid algorithm for DWT, second stage and DWPT 207
Pyramid algorithm for DWT, second stage, summary 93
Pyramid algorithm for MODWT 175
Pyramid algorithm for MODWT, first stage 164—165
Pyramid algorithm for MODWT, general stage 174—175 177 201
Pyramid algorithm for MODWT, inverse 175 177 203
Pyramid algorithm for MODWT, pseudo-code 177 204
Pyramid algorithm for MODWT, pseudo-code, pseudo-code for inverse 178 204
QMF see "Quadrature mirror filter"
Quadrature mirror filter (QMF) 75 151 163 498
Quadrature mirror filter (QMF) for time reversed filters 474 497
Quadrature mirror filter (QMF), alternative definition 79
Quartiles 442
Rabiner, L.R. 450—451 560
Rainfall average 6
Random circular shift 356 358 361 389 391
Random run 288 294
Random run, simulation 289
Random variable (RV) 256
Random variable (RV), binary-valued 410 454
Random variable (RV), continuous 256
Random variable (RV), discrete 256
Random variable (RV), mean of 256
Random variable (RV), mean of function of 256
Random variable (RV), multivariate 393
Random variable (RV), multivariate, Gaussian (normal) 400 407 441
Random variable (RV), outcome 256
Random variable (RV), realization 256
Random variable (RV), variance of 256
Random variables (RVs), independent 258
Random variables (RVs), independent and identically distributed (IID) 262
Random vector 393 258
Random walk process 288 293 385
Random walk process and DFBM 288
Random walk process, as first order backward difference of random run 294
Random walk process, nonstationary process with stationary first order backward difference 288
Random walk process, simulation of 289
Random walk process, wavelet variance for 337
Rao, C.R. 204 560 562
Rao, K.R. 54 560
Raphael, L. 554
Raymond, G.M. 560
Real component of complex variable 20
Real numbers (set of R) 457
Realization of RV 256
Reciprocity relationships 216
Reduced log likelihood for Gaussian FD process 363 389
Reduced log likelihood for instantaneous estimation 374
Reduced log likelihood for Nile River minima 386
Reduced log likelihood, using Gaussian nonboundary DWT coefficients 371 383
Reflecting boundary conditions 19 53 194
Reflecting boundary conditions and best basis selection 227—228
Reflecting boundary conditions and best shift basis selection 228
Reflecting boundary conditions for DWPT 227
Reflecting boundary conditions for DWT 140 433 439
Reflecting boundary conditions for MODWT 310
Reflecting boundary conditions, example with electrocardiogram 140 142
Regular DWT (alternative name for DWT) 218
Regularity 457
Regularity of function 486
Regularity of signal 486
Regularity, Hoelder 487
Regularization of the SDF 297—298
Reid, N. 434 560
Reinsel, G.C. 553
Relative approximation error 395 397
Rescaled wavelet function (alternative formulation for Haar) 10
Resolution of identity 205
Reversal of frequency order due to down-sampling with DWPT 211
Reversal of frequency order due to down-sampling with wavelet coefficients 85—86
Rice, S. 434 558
Richardson, G.A. 561
Riedel, K.S. 273—274 561
Riemann integral 6
Riemann sum 464
Rioul, O. 56 102—103 487 494 561
Risk 403 408
Risk function 265
Risk, minimum unbiased 402
RMSE see "Root mean square error"
Roberts, D.E. 264 553
Robinson, E.A. 488 561
Robinson, P.M. 379 561
Rocca, F. 411—412 415 556
Root mean square error (RMSE) 364 372 377 379 386 436
Root mean square error (RMSE), thresholding of log multitaper estimator 445
Rotated cumulative variance 189 294 382
Rotated cumulative variance for subtidal sea levels 189—190
Rothrock, D.A. 558
Roughs, Fourier 50—51 54
Roughs, wavelet 66
Roughs, wavelet, D(4) 65—66
Roughs, wavelet, Haar 64 66
Rubin, D.B. 555
Ruskai, M.B. 554
Rutman, J. 7 321 561
Rv see "Random variable"
Saddlepoint method 434 436
Salesin, D.H. 561
Sample ACS, FD process 341 350
Sample ACS, time series 14—15
Sample ACS, wavelet coefficients 14 16 19 343
Sample mean 16 48
Sample mean and DCT-II 55
Sample mean and DCT-IV 55
Sample mean and scaling coefficient 62 67 97 146 355
Sample mean of DWPT coefficients for node (j,n) 253
Sample mean of DWT coefficients 158
Sample mean of MODWT details and smooth 205
Sample mean of MODWT scaling coefficients 171
Sample mean, padding with 338
Sample mean, variance 293
Sample variance 48
Sample variance of MODWT scaling coefficients of  level 171
Sample variance of wavelet coefficients 344
Sample variance, bias in 299—300
Sample variance, decomposition of via DWT 62 67
Sample variance, decomposition of via MODWT 171 180 205
Sample variance, decomposition of via partial DWT 104
Sample variance, decomposition of via wavelet details 66—67
Sampled sinusoid signal 395
Sampling interval 48 59 266 315
Sampling interval, for FGN 285
Sapatinas, T. 552
Sardy, S. 560
Saulnier, G. 559
SCALE 6—7 58
Scale for scaling coefficients ( ), DWT 85 103 150
Scale for scaling coefficients (), MODWT 174
Scale for wavelet coefficients ( ), DWT, 59 67—68 85 103 150 206
Scale for wavelet coefficients (), MODWT 174
Scale, dyadic 13 15
Scale, physical 15 59 128 134 185
Scale, physical, for Nile river minima 192
Scale, physical, for subtidal sea levels 188 243
Scale, physical, for vertical ocean shear 194
Scale, unitless/standardized 59
Scale-by-scale ANOVA 62 151
| Scale-restricted MLE 373 385
Scaled chi-square distribution 313 336 338
Scaling coefficients 13 17 59
Scaling coefficients and long memory property with FD process 351
Scaling coefficients and sample mean 62 67 97 146 355
Scaling coefficients with DWT-based MLEs for Gaussian FD process 366
Scaling coefficients, boundary elements 136 146 158
Scaling coefficients, downsampling and bandwidth 84 86
Scaling coefficients, MODWT, boundary elements 198
Scaling coefficients, MODWT, compared to smooth of jth level 180 185
Scaling coefficients, MODWT, via circular filtering 163 169—170 173 175 177 200—201
Scaling coefficients, scale 464 495
Scaling coefficients, scale four 463
Scaling coefficients, scale two 462 495
Scaling coefficients, scale unity 460 464 495
Scaling coefficients, variance of 355
Scaling coefficients, via circular filtering 77 79—80
Scaling coefficients, via circular filtering for jth level 94 97 152
Scaling coefficients, via circular filtering for second level 88
Scaling filter 56 75 78 151 463 495
Scaling filter and father wavelet filter 80
Scaling filter of 4th level, shift factor for LA(8) 179
Scaling filter of 4th level, shift factor for LA(L) 158
Scaling filter of jth level 96 152
Scaling filter of jth level for C(6) 125
Scaling filter of jth level for D(4) 97—98
Scaling filter of jth level for DWT/MODWT 173
Scaling filter of jth level for LA(8) 97—98
Scaling filter of jth level, advance required for 118 156
Scaling filter of jth level, alternative formulations 102
Scaling filter of jth level, autocorrelation width 103 174
Scaling filter of jth level, connection to scaling function 469 496
Scaling filter of jth level, shift factor for C(L) 124 198 205
Scaling filter of jth level, shift factor for LA(L) 114 198 205
Scaling filter of jth level, squared gain function 157
Scaling filter of jth level, transfer function 97 152 157
Scaling filter of jth level, width 97
Scaling filter of second level 91—92
Scaling filter of second level, Daubechies and low-pass nature 91
Scaling filter of second level, Haar 40
Scaling filter of second level, nonorthogonality to even shifts 92
Scaling filter, advance required for LA(L) 113
Scaling filter, approximately linear phase for C(L) 124
Scaling filter, approximately linear phase for LA(L) 112 117
Scaling filter, BL(L) see "Best localized filter"
Scaling filter, coefficients for C(6) 109
Scaling filter, coefficients for D(4) 75 490
Scaling filter, coefficients for D(6), 106 109 491
Scaling filter, coefficients for D(8) 106 109 493
Scaling filter, coefficients for D(L) 493
Scaling filter, coefficients for Haar 75 463 489
Scaling filter, coefficients for LA(12) 109 112
Scaling filter, coefficients for LA(16) 109 112
Scaling filter, coefficients for LA(8) 109 112 494
Scaling filter, even width 75 78
Scaling filter, Fourier transform of time reversed 465 484 496
Scaling filter, Haar squared gain function 73 76
Scaling filter, key properties 154 499—500
Scaling filter, low-pass nature of Daubechies 76 78 151
Scaling filter, MODWT 169 200 469 476
Scaling filter, MODWT, autocorrelation width 174
Scaling filter, MODWT, connection to scaling function 469 496
Scaling filter, MODWT, energy 163
Scaling filter, MODWT, key properties 202
Scaling filter, MODWT, non-zero sum 163
Scaling filter, MODWT, orthogonality to even shifts 163
Scaling filter, MODWT, periodized 168 170 201
Scaling filter, MODWT, squared gain function 163
Scaling filter, MODWT, transfer function 163 169 173 201 469
Scaling filter, MODWT, width 169 201
Scaling filter, nonzero sum 76 78 151
Scaling filter, orthogonality to even shifted wavelet filter 77 151
Scaling filter, orthogonality to even shifts 76 78 151
Scaling filter, periodized 77 79—80 88
Scaling filter, periodized and circularly shifted 77 79
Scaling filter, reversal, of BL(14) from Doroslovacki 119
Scaling filter, reversal, of C(6) from Daubechies 123
Scaling filter, reversal, of LA(10), LA(14) and LA(16) from Daubechies 117
Scaling filter, shift factor for C(L) 124 229
Scaling filter, shift factor for LA(L) 229
Scaling filter, squared gain function 76 78 151
Scaling filter, squared gain function of time reversed 485 498
Scaling filter, support of scaling function 465
Scaling filter, time reversed 463 495
Scaling filter, transfer function 76 78
Scaling filter, unit energy 76 78
Scaling function 457 459 495
Scaling function, computation for D(4) 469
Scaling function, connection to scaling filter of jth level 469 496
Scaling function, finite support 465 472 496
Scaling function, Fourier transform of 465 468—469 496
Scaling function, Haar 460—463 479
Scaling function, integral of unity 468
Scaling function, key properties 499—500
Scaling function, normalization 468
Scaling function, support via scaling filter 465
Scaling function, two-scale relationship 464 466 470 495
Scargle, J.D. 295 561
Schafer, R.W. 28 106 117 484 560
Scher, M.S. 561
Schick, K.L. 340 561
SDF see "Spectral density function"
Sea surface temperature average 6—7
Seasonally dependent variation 188—189
Second backward difference 60
Second level details and smooths 89
Second order stationarity 266
Self-similarity parameter 279
Sequency (sequential frequency) ordering binary vector for node (j,n) 215—217 249 253
Sequency (sequential frequency) ordering binary vector for node (j,n), for MODWPT coefficients 232
Sequency (sequential frequency) ordering binary vector for node (j,n), for wavelet packet coefficients 209—212
Serroukh, A. 303 310 334 561
Shark's fin, 97 124 129 196 420 471
Shensa, M.J. 159 561
Shift invariant DWT 159
Shifted Haar wavelet function (alternative formulation), 9 10
Shimomai, T. 6 561
Short-Time Fourier Transform 206
Shrinkage 394 408 434 453
Shrinkage and nonlinear transform 408 411—412
Shrinkage, rules for 411 454
Shrinkage, rules for, approximate conditional median 411 415—416
Shrinkage, rules for, Bayesian 412—413 415 426—428 454
Shrinkage, rules for, conditional mean 411—412 424—426
Shrinkage, wavelet 412 417 454
Sidorenko, A. 273—274 561
Sign function 400
Signal, average value over a scale 6
Signal, continuous time 457
Signal, detail for finite energy 479 497
Signal, deterministic 394 398 417 452—453
Signal, dilation 457—458 474 494
Signal, DWT coefficients, independent 451
Signal, DWT coefficients, non-Gaussian 450
Signal, estimation 17 393
Signal, finite energy 457 459
Signal, inverse dilation 459
Signal, jth level detail for finite energy 480 497
Signal, jth level wavelet coefficients for finite energy 480 497
Signal, linear estimator 408
Signal, MRA for finite energy 478—479 481—482 496
Signal, nonlinear estimator 408
Signal, plus noise model 398 402 452
Signal, reconstruction via CWT 11
Signal, regularity 457 486
Signal, representation via DWT 394—395
Signal, sampled sinusoid, bump and sum 395
Signal, sparse 411 415
Signal, square integrability condition (real-valued) 458 494
Signal, stochastic 393—394 408 412 424 452 454
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