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| Percival D.B., Walden A.T. — Wavelet methods for time series analysis |
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| Предметный указатель |
Circular filtering of a finite sequence 31—32 55 268 296 336
Circular filtering with periodogram 433
Circular filtering, boundary effects 136 139 145 197 227
Circular filtering, DWPT coefficients 210—212
Circular filtering, DWPT coefficients for node (j,n) 214—215 249—250
Circular filtering, DWT coefficients 70 74 77 79 80 88 92 94—97 152
Circular filtering, MODWPT coefficients 232
Circular filtering, MODWPT coefficients for node (j,n) 231 251
Circular filtering, MODWT coefficients 163 168—170 173 175 177 200—201
Circular shift matrix 52 71
Circular shift matrix, inverse 52
Circular shift, random 356 358 361 389 391
Circular shift, rows of DWT matrix 59
Circular/reflecting boundary conditions, electrocardiogram 133 140
Circularity 52
Circularly shifted series 52 429
Circularly shifted series, best basis algorithm 227
Circularly shifted series, discrete Fourier empirical power spectrum 52
Circularly shifted series, discrete wavelet empirical power spectrum 63
Circularly shifted series, Fourier coefficients 52
Circularly shifted series, Fourier details 55
Circularly shifted series, MODWT of 179 181
Circularly shifted series, MRA via MODWT 181
Circularly shifted series, MRA via partial DWT 160—161
Circularly shifted series, partial DWT of 160—161
Circularly shifted series, wavelet details of jth level 191
Cleveland, W.S. 272 554
Clustering of DWT coefficients 450—451 455
Clustering of DWT coefficients, ECG 450
Coarse approximation, scale  464 495 500
Coarse approximation, scale four 463
Coarse approximation, scale two 462 495
Coble, P.A. 561
Cohen, A. 141 554
Coiflets 123 see
Coiflets, embedded backward differencing 124 156 306
Coiflets, squared gain function 124
Coifman, R.R. 144 159 204 215 223 225 374 429 554
Complex conjugate, complex variable 21
Complex conjugate, DFT 22
Complex demodulation 22 39
Complex exponential 21—22
Complex orthonormal matrix (unitary) 45 53
Complex variable 20
Complex variable, absolute value 21
Complex variable, argument 21
Complex variable, Cartesian representation 21
Complex variable, complex conjugate 21
Complex variable, complex exponential 21
Complex variable, de Moivre's theorem 21
Complex variable, Euler relationship 21 48
Complex variable, imaginary component 20—21
Complex variable, magnitude 21
Complex variable, modulus 21
Complex variable, polar representation 21
Complex variable, real component 20—21
Complex-valued transform 41 45 53
Complex-valued wavelet function 4
Complex-valued wavelet function, Morlet 5
Compo, G.P. 12 295 303 562
Conditional expectation see "Conditional mean"
Conditional mean 260 266 394 408—411 414—415 454 456
Conditional mean in geophysics 411
Conditional mean, estimator 261
Conditional mean, LA(8) partial DWT 425—426
Conditional mean, shrinkage rule 411—412 424
Conditional median 266 394 408 411 415 454
Conditional median, estimator 261
Conditional median, shrinkage rule (approximate) 412 415—416
Conditional pdf 260 409
Conditionally Gaussian 461
Confidence intervals for SDF 275 278
Confidence intervals for time-dependent wavelet variance 325
Confidence intervals for wavelet variance 311 313—314 319—320 327 332—334 336 345 385
Confidence intervals for wavelet variance, atomic clock average fractional frequency deviates 322—323
Consistent estimator and hard thresholding 456
Consistent estimator of SDF 271—272
Constantine, W. 360 369 560
Continuity of function and its derivatives 486
Continuous parameter 266
Continuous parameter nonstationary process 340 354
Continuous parameter nonstationary process, simulation 361
Continuous parameter pure power law process 285
Continuous RV 256
Continuous wavelet transform (CWT) 1 457
Continuous wavelet transform (CWT), energy decomposition 11
Continuous wavelet transform (CWT), first derivative of Gaussian 10
Continuous wavelet transform (CWT), grey-scaled 8 11
Continuous wavelet transform (CWT), Haar 10 13
Continuous wavelet transform (CWT), Mexican hat 8 11
Continuous wavelet transform (CWT), reconstruction of a signal 11
Continuous wavelet transform (CWT), versus DWT 1 13
Contreras Cristan, A. 217 239 247 563
Convolution (circular) of finite sequences 29—31 37
Convolution (circular) of finite sequences, DFT of 30 37 52 72
Convolution and filtering 25
Convolution of functions 38
Convolution of functions, Fourier transform of 38
Convolution of infinite sequences 24 36
Convolution of infinite sequences, DFT of 24 36
Coordinated Universal Time (UTC) 317
Coronal Mass Ejection (CME) 220 237
Corotating interaction region (CIR) 219 237
Correlated Gaussian noise 417
Correlated Gaussian wavelet coefficients 440
Correlated noise 393
Correlated noise DWT coefficients 440
Correlated noise DWT coefficients, level-dependent variance 441 456
Correlation 259
Correlation matrix, DWT coefficients and FD process 349
Correlation matrix, DWT coefficients and FD process, D(4) 351
Correlation matrix, DWT coefficients and FD process, Haar 350
Correlation matrix, DWT coefficients and FD process, LA(8) 351
Correlation, Haar 347
Correlation, LA(8) 347
Correlation, nonboundary wavelet coefficients at different levels 346
Cost functional see "Additive cost functional"
Covariance 259 266 293
Covariance matrix 259 262
Covariance matrix, approximation via DWT coefficients 355 389
Covariance matrix, circular 441
Covariance matrix, determinant of 361
Covariance matrix, DWT coefficients 349 355
Covariance matrix, error in WLSE 376
Covariance matrix, FD process 355
Covariance matrix, IID noise 393 452
Covariance matrix, non-IID noise 393 453
Covariance matrix, signal vector 393
Covariance matrix, simulated for FD process 356
Covariance matrix, WLSE parameter estimates 376
Covariance of stationary stochastic process 266
Covariance, log multitaper SDF estimator 276 277
Covariance, nonboundary wavelet coefficients at different levels 345 348
Covariance, nonboundary wavelet coefficients at same level 345 348
Covariance, periodogram 270—271
Craigmile, P.F. 368 371 554
Cramer — Rao lower bound 364 386
Cross-correlation (circular) of finite sequences 30—31 37 234
Cross-correlation (circular) of finite sequences, DFT of 30 37 39 234
Cross-correlation (circular) of finite sequences, interleaving for wavelet details and smooths 82
Cross-correlation (circular) of finite sequences, MODWPT details for node (j,n) 234 251
Cross-correlation (circular) of finite sequences, MODWT details and smooths 167 172 203
Cross-correlation (circular) of finite sequences, periodized scaling and wavelet filters 77
Cross-correlation (circular) of finite sequences, upsampling for wavelet details and smooths 82—83
Cross-correlation of functions 38
Cross-correlation of functions, Fourier transform of 38
Cross-correlation of infinite sequences 24 36
Cross-correlation of infinite sequences, DFT of 25 36 39
Cross-validation 402 453
Cross-validation, leave-one-out 402
| Cross-validation, leave-one-out using DWT 422
Cross-validation, two-fold 402
Cross-validation, two-fold using partial DWT 422
Crouse, M.S. 450—452 455 554
Cumulative distribution function, Gaussian (normal) 257
Cutler, L.S. 553
CWT see "Continuous wavelet transform"
Cycle spinning 144 204 374 429
Cycle spinning and the MODWT 429
Cyclic see "Circular"
Cyclic filter see "Circular filtering"
Czerny, B. 340 559
D(4) DWT matrix 59—60
D(4) scaling filter 75 490
D(4) scaling filter of jth level 97—98
D(4) scaling filter of jth level, connection to scaling function 471
D(4) scaling filter, squared gain function 73 76
D(4) scaling filter, squared gain function, of second level 91
D(4) wavelet filter 59 155
D(4) wavelet filter, as a filter cascade 68
D(4) wavelet filter, jth level 97—98 157
D(4) wavelet filter, jth level, connection to wavelet function 478
D(4) wavelet filter, jth level, phase function 158
D(4) wavelet filter, phase function 158
D(4) wavelet filter, squared gain function 73
D(4) wavelet filter, squared gain function, of second level 91 157
D(6) scaling filter 106 109 491
D(8) scaling filter 106 109 493
D(L) scaling and wavelet functions D(4), computation 469 477
D(L) scaling and wavelet functions D(4), connection to jth level filters 471 478
D(L) scaling and wavelet functions D(4), Hoelder regularity 487 494
D(L) scaling filter 106 117 155 493
Dahlquist, G. 280 554
Daniels, H.E. 434 554
Das, p. 559
Data tapers 53 273
Data tapers, orthonormal 273
Data tapers, sine 274 277 440
Daubechies scaling filter, BL method 119
Daubechies scaling filter, extremal phase 108 117
Daubechies scaling filter, least asymmetric 107 112 117
Daubechies scaling filter, phase function 106
Daubechies scaling filter, squared gain function 105 116 155
Daubechies scaling filter, squared gain function, of time reversed 486 498
Daubechies scaling filter, transfer function 106
Daubechies wavelet filter, as a filter cascade 105 107
Daubechies wavelet filter, construction of 457
Daubechies wavelet filter, embedded backward differencing 306
Daubechies wavelet filter, from extremal phase scaling filter 108
Daubechies wavelet filter, high-pass nature 73—74 151 158
Daubechies wavelet filter, L/2 embedded differences 106 123—124 155
Daubechies wavelet filter, low-pass filter component 106 155
Daubechies wavelet filter, of jth level, sidelobes of squared gain function 123
Daubechies wavelet filter, of jth level, squared gain function 121—122
Daubechies wavelet filter, squared gain function 105 116 153
Daubechies wavelets 59 442
Daubechies, T. 4 105—106 108—109 112—113 117—118 123 153 457 461 468 472 476 483 486—487 492—493 498 546 554
Daublets 106
David, H.A. 299 555
Davies — Harte simulation method 281 283 290—291 341
Davies, R.B. 290 555
Davis, G. 239 363 367 555
Davis, R.A. 553
Davison, A.C. 434 555 560
Day, N.L. 561
DCT see "Discrete cosine transform"
De Moivre's theorem 21
Decibel (dB) scale 121 273
Decorrelation via the DWT 16 19 341
Decorrelation via the DWT of AR(1) process 353
Decorrelation via the DWT of FD process 340 345 350 380 388
Decorrelation via the DWT of MA(1) process 391
Degrees of freedom 270
Del Marco, S. 159 174 228 555
Denoising 393
Denoising, nuclear magnetic resonance, using LA(8) partial DWT 431
Denoising, nuclear magnetic resonance, using ODFT 431
Deo, R. 557
Deriche, M. 562
DeRose, T.D. 561
Detail for finite energy function (signal) 479—480 497
Detail space, Haar, scale one half 475
Detail space, Haar, scale one quarter 475
Detail space, Haar, scale unity 475
Detail space, scale  472 496
Details, boundary elements 139 147 199
Details, DWT 64—65 151 158
Details, DWT, D(4) 65—66
Details, DWT, first level 81
Details, DWT, Haar 64—65
Details, DWT, jth level 95 191
Details, DWT, second level 89
Details, Fourier 50—51 54—55
Details, MODWPT and zero phase 234 237 252
Details, MODWPT for node (j,n) via cross-correlation (circular) 234 251
Details, MODWT and DWT averaging 204—205
Details, MODWT and zero phase 160 168 172 189
Details, MODWT via cross-correlation (circular) 172 203
Details, MODWT, jth level 171 173 176—177 191 200 203
Determinant of approximate covariance matrix 362
Determinant of covariance matrix 361
Deterministic signal 393—394 398 417 452—453
Deterministic signal, estimation via thresholding 398
DFBM see "Discrete fractional Brownian motion"
DFT see "Discrete Fourier transform"
DHM see "Davies — Harte simulation method"
DICTIONARY 239 252 254
Dictionary, element of 239
Dictionary, MODWT and constant vectors 247
Dictionary, MODWT and ODFT vectors 247
Dictionary, MODWT vectors 242 253
Dictionary, orthonormal 240
Dictionary, partial DWT vectors 240
Dictionary, redundant 241—242
Dictionary, renormalized MODWT vectors 242—243
Dictionary, WP table and ODFT vectors 241
Dictionary, WP table vectors 241 254
Differentiability (weak) 403—404 456
Digamma function 275 376 390 440
Dijkerman, R.W. 354 555
Dilation 457—458 474
Dilation, dyadic 458 494
Dilation, inverse dyadic 459
Dilation, non-commuting with translation 459
Dipole filter 488
Direct spectrum estimator 273
Direct sum 472
Direct sum, approximation and detail spaces 482
Direct sum, illustrated for Haar scaling function 472—473
Discrete cosine transform (DCT) 41 54
Discrete cosine transform (DCT), type II transform (DCT-II) 54
Discrete cosine transform (DCT), type IV transform (DCT-IV) 54
Discrete Fourier empirical power spectrum 48—49 55
Discrete Fourier empirical power spectrum, invariance to shifts 52
Discrete Fourier transform (DFT) 17 22
Discrete Fourier transform (DFT) and ODFT 52 54
Discrete Fourier transform (DFT), autocorrelation 25 36
Discrete Fourier transform (DFT), circular autocorrelation 30 37
Discrete Fourier transform (DFT), circular convolution 30 37 52
Discrete Fourier transform (DFT), circular cross-correlation 30 37 39 234
Discrete Fourier transform (DFT), complex conjugate 22
Discrete Fourier transform (DFT), convolution 24 36
Discrete Fourier transform (DFT), cross-correlation 25 36 39
Discrete Fourier transform (DFT), even indexed subsequence 23
Discrete Fourier transform (DFT), finite sequence 28 36
Discrete Fourier transform (DFT), finite sum of squared magnitudes 21
Discrete Fourier transform (DFT), finite/infinite sequences 28
Discrete Fourier transform (DFT), infinite sequence 22 35 39
Discrete Fourier transform (DFT), inverse for finite sequence 29 36 78 291
Discrete Fourier transform (DFT), inverse for infinite sequence 22 35 70
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