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| Percival D.B., Walden A.T. — Wavelet methods for time series analysis |
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| Предметный указатель |
Multiresolution analysis (MRA), via partial DWT 104 129
Multitaper SDF estimator 269 273 329—330 394 439
Multitaper SDF estimator, applied to solar physics series 278
Multitaper SDF estimator, bandwidth of 274 277—278
Multitaper SDF estimator, lack of leakage 330 446
Multitaper SDF estimator, logarithm of 276 444
Multivariate RV 393
Multivariate RV, Gaussian (normal) 400 407 441
Munk, W.H. 340 559
Musha, T. 340 559
Nanoseconds 318
Nanoteslas (nT) 219
Narrow-band frequency characteristic 396
Nason, G.P. 159 402 421—423 559
Natural ordering for wavelet packet coefficients 209—210
Negative frequency 22
Nested subspaces 460 494
Nested subspaces, approximation and detail spaces 472—473
Nested subspaces, convention for approximation spaces 461
Neugebauer, M. 556 564
Nguyen, T. 465 471 562
Nile River minima 255 295 326 341 365 386
Nile River minima, change point 387—388
Nile River minima, MLE for 386
Nile River minima, MLE for, using Haar, D(4) and LA(8) filters 392
Nile River minima, MRA for Haar MODWT 190 192
Nile River minima, physical scales 192
Nile River minima, test for homogeneity of variance 386—387
Nile River minima, wavelet variance estimates for 327
Nilometer 193
NMR see "Nuclear magnetic resonance"
Noise DWT coefficients, correlated 440
Noise DWT coefficients, IID Gaussian (normal) 418
Noise DWT coefficients, non-IID 432 434
Noise DWT coefficients, PDFs with level 455
Noise DWT coefficients, stochastic 424 426
Noise DWT coefficients, uncorrelated 432 434
Noise transform coefficients 394 406—408 412 452
Noise transform coefficients, IID Gaussian 453
Noise transform coefficients, non-IID 403
Noise vector, IID 452
Noise vector, non-IID 452
Noise, correlated 393
Noise, Gaussian (normal) 440
Noise, IID 393 398 451—452
Noise, IID Gaussian (normal) 417
Noise, non-Gaussian 432
Noise, non-IID 393 402
Noise, uncorrelated 393
Non-decimated DWT 159
Non-Gaussian noise 432
Non-Gaussian signal DWT coefficients 450
Non-IID noise DWT coefficients 432 434
Non-IID noise transform coefficients 403
Nonboundary DWT coefficients 370
Nonboundary DWT coefficients, MLE 371—372 383—384 390
Nonboundary DWT coefficients, reduced log likelihood 371 383
Nonlinear conditional mean 417
Nonlinear estimator of signal 408
Nonlinear transform and shrinkage 408 411—412 454
Nonnegative garrote 456
Nonorthogonality of MODWT 159
Nonstationary process 1/f-type 287
Nonstationary process with nonstationary first order backward difference 294
Nonstationary process with Pth order trend plus stationary process 289 294
Nonstationary process with stationary dth order backward difference 287 368
Nonstationary process with stationary dth order backward difference, SDF 287
Nonstationary process with stationary dth order backward difference, simulation 292
Nonstationary process with stationary first order backward difference, random walk 288
Nonstationary process with stationary first order backward difference, trend plus stationary process 288
Nonstationary process with stationary second order backward difference, random run 294
Nonstationary process, continuous parameter 340
Nonstationary process, example simulation via DWT 360
Nonstationary process, long memory 284 286
Nonstationary process, long memory, DWT-based MLEs for 368
Nonstationary process, long memory, FD 284 288
Nonstationary process, long memory, PPL 281
Nonstationary process, simulation 289
Nonstationary process, simulation, via DWT 360
Normal PDF see "Gaussian PDF"
Normal RVs see "Gaussian RVs"
Normalization and periodized filters 34
Normalization of scaling function 468
Normalized partial energy sequence (NPES) 129 395
Normalized partial energy sequence (NPES) for electrocardiogram 128—129
Normalized partial energy sequence (NPES) for signals 395—396
Normalized partial energy sequence (NPES) for vertical ocean shear 397
Normalized partial energy sequence (NPES), using DWT coefficients 128—129 395—396 455
Normalized partial energy sequence (NPES), using ODFT coefficients 128—129 395—396
Nowak, R.D. 554
NPES see "Normalized partial energy sequence"
Nuclear magnetic resonance (NMR) 420 424 427
Nuclear magnetic resonance (NMR), Bayesian shrinkage estimates of signal 428
Nuclear magnetic resonance (NMR), denoising, using LA(8) partial DWT 431
Nuclear magnetic resonance (NMR), denoising, using ODFT 431
Nuclear magnetic resonance (NMR), MODWT-based thresholding estimates of signal 430
Nuclear magnetic resonance (NMR), shrinkage estimates of signal 425—426
Nuclear magnetic resonance (NMR), thresholding estimates of signal 418—419 421 423
Nyquist frequency 22 87 267 315
O'Brien, J.J. 559
Octave band average, FD process 343 353
Octave band SDF estimation 316 329—330 337 343 389
Octave band-pass filter 102
Octave frequency band 297
Odd indexed subsequence and DFT 39
Odegard, J.E. 558
ODFT see "Orthonormal discrete Fourier transform"
Ogden, R.T. 135 255 560
Oppenheim, A.V. 28 106 117 366 484 560 563
Oppenheim, G. 552 554 559
Optimal discrete WP table transform 223 251
Optimal discrete WP table transform, example of 224
Oracle 420
Ordinary least squares estimation for FD process 378
Orthogonal complement 472 496
Orthogonality principle of linear mean, square estimation 407
Orthonormal basis, approximation space with scale  460 495
Orthonormal basis, approximation space with scale one half 461
Orthonormal basis, approximation space with scale two 461
Orthonormal basis, approximation space with scale unity 459
Orthonormal basis, detail space with scale one half 474—475 496 500
Orthonormal basis, detail space with scale one quarter 475
Orthonormal basis, detail space with scale unity 475
Orthonormal data tapers 273
Orthonormal discrete Fourier transform (ODFT) 41 46 49 53 395 431
Orthonormal discrete Fourier transform (ODFT) and DFT 52 54
Orthonormal discrete Fourier transform (ODFT), energy preservation 47
Orthonormal discrete Fourier transform (ODFT), inverse 49
Orthonormal discrete Fourier transform (ODFT), matrix 47
Orthonormal discrete Fourier transform (ODFT), projection theorem 52
Orthonormal matrix 42—43 53
Orthonormal transform 41 394 452
Orthonormal transform of IID Gaussian RVs 263 400
Orthonormal transform of noise coefficients 394 398 406
Orthonormal transform of signal coefficients 394 398
Orthonormal transform, DWT 57 67 72
Orthonormal transform, energy preservation 43 53
Orthonormal transform, projection theorem 44 53
Orthonormality and DWT 76—77 79 95
Orthonormality property of wavelet filty 69
Outcome of RV 256
PACS (partial autocorrelation sequence) 367
Padding (extending a sample) for the DWT 141 422—423
Padding (extending a sample) with sample mean 338
Padding (extending a sample) with zeros 308 338 382 387
Padding (extending a sample) with zeros, for the FFT 440
Papoulis, A. 256 560
Paradigm for wavelet thresholding 444 449 455
Parameter and properties of DFBM process 286
Parameter and properties of FD process 285—286
| Parameter and properties of FGN process 285—286
Parameter and properties of PPL process 285—286
Parameter estimation for FD process via DWT coefficients 341
Parent node for DWPT 210
Parks, T.W. 159 174 558
Parseval's theorem 23 312 314
Parseval's theorem, one finite sequence 29 36 72 170 233
Parseval's theorem, one function 38
Parseval's theorem, one infinite sequence 23 35
Parseval's theorem, two finite sequences 29 36 233
Parseval's theorem, two functions 38 467
Parseval's theorem, two infinite sequences 23 35
Partial autocorrelation sequence (PACS) 367
Partial discrete wavelet transform (DWT) 19 56 80 104 211 341 350 385 418 433 445 447 451 454
Partial discrete wavelet transform (DWT) of ECG data 126
Partial discrete wavelet transform (DWT) of FD process 342
Partial discrete wavelet transform (DWT), advanced LA(8) coefficients for electrocardiogram 127—128
Partial discrete wavelet transform (DWT), atomic clock data 13
Partial discrete wavelet transform (DWT), C(6) 126
Partial discrete wavelet transform (DWT), choice of level 145
Partial discrete wavelet transform (DWT), circularly shifted series 160—161
Partial discrete wavelet transform (DWT), D(4) 126 418 420
Partial discrete wavelet transform (DWT), decomposition of sample variance 104
Partial discrete wavelet transform (DWT), disjoint dyadic decomposition of WP table 212
Partial discrete wavelet transform (DWT), energy decomposition 15 16 95 104 151
Partial discrete wavelet transform (DWT), Haar 13—14 55 126
Partial discrete wavelet transform (DWT), inverse 419 422 425 433—434 445 454
Partial discrete wavelet transform (DWT), LA(8) 126 418—421 423—425 428 431
Partial discrete wavelet transform (DWT), LA(8), basis vectors 162
Partial discrete wavelet transform (DWT), level of 56
Partial discrete wavelet transform (DWT), matrix 79
Partial discrete wavelet transform (DWT), multiple of power of two length 104 141 150
Partial discrete wavelet transform (DWT), vectors for waveform dictionary 240
Partial DWT see "Partial discrete wavelet transform"
Partial energy sequence 106
Partial energy sequence for maximum/minimum delay filter 488 493
Parzen, E. 272 554
PDF see "Probability density function"
Penalty term 398
Percentage points for homogeneity of variance test 381
Percentage points for trend test 373
Percentage points of chi-square PDF 264
Percentage points of standard Gaussian (normal) PDF 257
Percival, D.B. 159 185 244 291—292 297 307 309—310 321 326 353—354 360 554 556 558—561 563
periodic extension 30
Periodicity of DFT for finite sequence 28 36
Periodicity of DFT for infinite sequence 22 35
Periodized filter 20 32—33 35 37 39—40
Periodized filter, DFT of 33—34 37 39
Periodized filter, DWT scaling filter 77 79—80 88
Periodized filter, DWT scaling filter, circularly shifted 77 79
Periodized filter, DWT scaling filter, DFT of 92 100
Periodized filter, DWT wavelet filter 71 74 80 88 92 96—97 153
Periodized filter, DWT wavelet filter, autocorrelation 72
Periodized filter, DWT wavelet filter, circularly shifted 71 77 92 153
Periodized filter, DWT wavelet filter, DFT of 92 100
Periodized filter, example 34
Periodized filter, MODWT scaling and wavelet filter 168—170 201
Periodized filter, normalization 34
Periodogram 269 298 312 314 330 394
Periodogram, asymptotic properties (independence and unbiasedness) 270
Periodogram, bias of 298
Periodogram, covariances of 270—271
Periodogram, inconsistency of 270 298
Periodogram, leakage in 272—273 329 437 439
Periodogram, logarithm of 270 432
Periodogram, mean of 270
Periodogram, smoothing of 271
Periodogram, variance of 270
Persistence of DWT coefficients 450—451 455
Pesquet, J.-C. 159 560
Peterson, S. 204 560
Phase function 25
Phase function, D(4) wavelet filter 158
Phase function, Daubechies scaling filter 106
Phase function, Haar wavelet filter 158
Phase function, LA(L) and C(L) wavelet packet filter for node (j,n) 229
Phase function, LA(L) scaling and wavelet filters 112
Phase function, wavelet packet filter for node (3,n) 253
Phillips, J.L. 556
Physical bandwidth for MODWPT of solar magnetic field 236
Physical frequency 221
Physical scale 15 59 128 134 185 243 297 315 328 334
Physical scale for MODWT details and smooth of jth level 188 192 194
Physical time width for MODWPT of solar magnetic field 236
Picard, D. 556
Piecewise power law process 321 323 328
Pilot spectrum estimator 297
Pilot spectrum estimator and unbiased Haar-based estimator 317
Point estimate 265
Polar representation of complex variable 21
Polynomial (trigonometric) 485
Popper, W. 193 560
Porter-Hudak, S. 379 555
Positive frequency 22
Posterior, expected loss 265
Posterior, mean 266 414 454
Posterior, median 266 415—416 454
Power law process 288 294 297 332 337 340
Power of two and DWT 57 67 141 150
Power of two, multiple of, and partial DWT 104 141 150
Power of two, needed with periodogram 437
Power spectrum for stationary process 267
Power spectrum, discrete Fourier empirical 48—49 55
Power spectrum, discrete wavelet empirical 160 181
Power spectrum, discrete wavelet empirical, DWT-based 62—63 66—67 156 297
Power spectrum, discrete wavelet empirical, MODWT-based 160 181
PPL process see "Pure power law process"
Press, W.H. 56 560
Priestley, M.B. 255—256 268—269 313 560—561
Prior information 264
Prior PDF 264—265
probability 256
Probability density function (pdf) 256
Probability density function (PDF), chi-square 263
Probability density function (pdf), conditional 260 409
Probability density function (PDF), exponential 265
Probability density function (PDF), Gaussian (normal) 3 256
Probability density function (PDF), generalized Cauchy (t) 258
Probability density function (PDF), generalized Gaussian 257
Probability density function (PDF), joint 258 265 409
Probability density function (PDF), jointly Gaussian (normal) 259
Probability density function (PDF), Laplace (two-sided exponential) 257 264
Probability density function (pdf), marginal 258 265
Probability density function (PDF), prior 264—265
Probability density function (PDF), sum of two independent RVs 262 409 416
Probability density function (PDF), sum of two RVs 262
Probability density function (PDF), t 257
Probability density function (PDF), transformed RVs 258 261
Probability of false alarm 435
Projection onto subspace 45
Projection theorem 41
Projection theorem, ODFT 52
Projection theorem, orthonormal transform 44 53
Projection theorem, unitary transform 46
Pseudo-code for DWT, analysis 101 157
Pseudo-code for DWT, details and smooth 102
Pseudo-code for DWT, pyramid algorithm 100
Pseudo-code for DWT, synthesis 101 157
Pseudo-code for MODWT, analysis 177 204
Pseudo-code for MODWT, details and smooth 179
Pseudo-code for MODWT, pyramid algorithm 177 204
Pseudo-code for MODWT, synthesis 178 204
Puccio, L. 555
Pure power law process, continuous parameter 285
Pure power law process, discrete parameter 281
Pure power law process, long memory property 281
Pure power law process, parameter and properties 285—286
Pure power law process, simulation 283
Pure power law process, spectral density function (SDF) 281—282
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