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Percival D., Walden A. — Spectral Analysis for Physical Applications
Percival D., Walden A. — Spectral Analysis for Physical Applications



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Название: Spectral Analysis for Physical Applications

Авторы: Percival D., Walden A.

Аннотация:

This book is an up-to-date introduction to univariate spectral analysis aimed at graduate students, which reflects a new scientific awareness of spectral complexity, as well as the widespread use of spectral analysis on digital computers with considerable computational power. The text provides theoretical and computational guidance on the available techniques, emphasizing those that work in practice. It gives equal weight to both algorithms and statistical theory and is valuable for the many examples it gives showing the application of spectral analysis to real data sets. The book is unique in placing special emphasis on the multitaper technique, which can successfully handle spectra with intricate structure and data with or without spectral lines. The text contains a large number of exercises.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 611

Добавлена в каталог: 09.03.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Data taper      206 223 542 see
Data window      206
Davis, R.A.      423 431 433 446 547
Day, N.L.      558
DC (direct current)      466
de Gooijer, J.G.      436—437 549
Decay of envelope of sidelobes      259
Decay, rate of sidelobes      261
Decay, rate of sidelobes, Bartlett lag window      266
Decay, rate of sidelobes, Daniell lag window      264
Decay, rate of sidelobes, Parzen lag window      266
Decaying sinusoids      500
Decibel scale      22 228 258 298
Default taper      207
Degenerate kernel      103
Degrees of freedom      221 254 293
Degrees of freedom in a time series      278
Degrees of freedom of order      2 278
Degrees of freedom, equivalent      255 292 472
Demeure, C.      332 552
Derivative as an LTI filter      183
Deterministic function      57
Deterministic sequence      57
Deterministic sinusoid      514 525
Detrending a time series      176
DFT      see "Discrete Fourier transform"
Diagonal matrix      375 412 535
Differencing for periodicity removal      52
Differencing for trend removal      52
Diggle, P.J.      305 549
Dirac delta function      133 144 160 183 475
Direct current (DC)      466
Direct spectral estimator      207 220 319 326 330 352 438 452 497
Direct spectral estimator and Yule — Walker autoregressive spectral estimator      396 405
Direct spectral estimator of harmonic components      486
Direct spectral estimator, AR(2) data      308
Direct spectral estimator, AR(4) data      313
Direct spectral estimator, bias of      213 227
Direct spectral estimator, correlation of      231—232
Direct spectral estimator, covariances of      223 230 326
Direct spectral estimator, discretely smoothed      236 287
Direct spectral estimator, distribution of      223 320
Direct spectral estimator, expected value of      206—207 320
Direct spectral estimator, inconsistency of      224
Direct spectral estimator, mean corrected      217 501
Direct spectral estimator, ocean wave data      296—297 440
Direct spectral estimator, relationship to quadratic spectral estimator      353
Direct spectral estimator, smoothing of      235
Direct spectral estimator, spectral window for      320
Direct spectral estimator, statistical properties of      220
Direct spectral estimator, use of in AR order selection      437
Direct spectral estimator, variability      226
Direct spectral estimator, variance of      223 320
Direct spectral estimator, white noise      348
Direct spectral estimator, Willamette River data      505 507
directionality      434
Dirichlet's kernel      26—27 90—92 102 113 124 150 198 362
Discrete Fourier transform (DFT)      110 235 284 323
Discrete Fourier transform (DFT) and chirp transform      114
Discrete Fourier transform (DFT) as a convolution      113
Discrete parameter sequence, convolution theorem      118
Discrete parameter sequence, Fourier representation      118
Discrete parameter sequence, Fourier transform      87
Discrete parameter sequence, Parseval's theorem      118
Discrete parameter sequence, segment of, convolution theorem      119
Discrete parameter sequence, segment of, Fourier representation      118
Discrete parameter sequence, segment of, Parseval's theorem      119
Discrete parameter sequence, segment of, spectral properties      119
Discrete parameter sequence, spectral properties      118
Discrete parameter stochastic process      32
Discrete power spectrum      60
Discrete power spectrum, Walsh method      163
Discrete prolate spheroidal sequence (dpss)      104 124 210 334
Discrete prolate spheroidal sequence (dpss), accuracy of computation      380 386
Discrete prolate spheroidal sequence (dpss), calculation of      378
Discrete prolate spheroidal sequence (dpss), calculation of, direct from defining equation      379
Discrete prolate spheroidal sequence (dpss), calculation of, using inverse iteration      381
Discrete prolate spheroidal sequence (dpss), calculation of, using numerical integration      384
Discrete prolate spheroidal sequence (dpss), calculation of, using tridiagonal formulation      386
Discrete prolate spheroidal sequence (dpss), calculation of, zeroth-order sequence      386
Discrete prolate spheroidal sequence (dpss), scaling and polarity      379
Discrete prolate spheroidal sequence (dpss), trig prolate approximations      387
Discrete prolate spheroidal sequence (dpss), zeroth-order as a filter      181
Discrete prolate spheroidal wave function (dpswf)      104 122 124 362 376
Discrete spectrum      141 456 460 489 540
Discretely smoothed direct spectral estimator      236 287
Distribution of adaptive multitaper spectral estimator      370 377
Distribution of direct spectral estimator      223 320
Distribution of lag window spectral estimator      254 322 449
Distribution of maximum likelihood AR parameter estimator      433
Distribution of multitaper spectral estimator      343 360
Distribution of periodogram      221—222 319
Dongarra, J.J.      558
Doodson, A.T.      457 549
Doppler measurements of blood flow      151
Doppler ultrasound      40
Double orthogonality of eigenfunctions      78 103
Double-sided spectral density function      140
dpss      see "Discrete prolate spheroidal sequence"
dpss taper      211—212 227 270 297 313 405 439 486 497 507 520
dpss taper, decomposition of energy      345
dpswf      see "Discrete prolate spheroidal wave function"
Duration-bandwidth product      79 335 384 390
Durbin, E.J.      556
Durrani, T.S.      552
Dynamic range      201 205 218 313 315 331 439
Dziuba, S.      52
Earthquake coda      70
Echoes      298
Eigenfunction      77
Eigenfunction for a linear filter      156
Eigenspectra      333 335 337 339 364 371 497
Eigenspectra, covariance of      350 375
Eigenvalues      77 534 536
Eigenvalues for a linear filter      156
Eigenvectors, left and right      534 536
EISPACK      379 387 389
Energy of a nonperiodic function      66
Energy of a periodic function      59
Energy spectral density function      66 153
Ensemble      31
Entire function      69
entropy      421
Envelope of sidelobes      264
Equal by definition      10
Equal in distribution      222
Equivalence of time and frequency domains      66
Equivalent degrees of freedom      255 257 292 322 370 442 472
Equivalent width      70 121 242 252
Ergodic theorems      189
Estimation of autocovariance sequence, complex variables      317
Estimation of autocovariance sequence, real variables      190
Estimation of mean      188
Estimation of spectral bandwidth      277
Euler relationship      25
Euler's constant      228 281
Exact conditional least squares, sinusoidal amplitude estimator      502
Exact conditional least squares, white noise variance estimator      502
Exact least squares      463 541
Exact least squares sinusoidal amplitude estimator, complex values      466
Exact least squares sinusoidal amplitude estimator, complex values, covariance of      466 543—544
Exact least squares sinusoidal amplitude estimator, complex values, expected value of      466 543
Exact least squares sinusoidal amplitude estimator, complex values, variance of      466 543
Exact least squares sinusoidal amplitude estimator, real values      463 541
Exact least squares sinusoidal amplitude estimator, real values, covariance of      464 541
Exact least squares sinusoidal amplitude estimator, real values, expected value of      463 541
Exact least squares sinusoidal amplitude estimator, real values, variance of      463 541
Exact least squares white noise variance estimator, complex values      466
Exact least squares white noise variance estimator, real values      464
Exact unconditional least squares, sinusoidal amplitude estimator      502
Exact unconditional least squares, white noise variance estimator      502
Example of an LTI digital filter      171
Expected value (expectation)      6
Expected value (expectation) of direct spectral estimator      206—207 320
Expected value (expectation) of lag window spectral estimator      243 321 327
Expected value (expectation) of multitaper spectral estimator      334
Expected value (expectation) of periodogram      198 319 324
Expected value (expectation) of quadratic spectral estimator      353 355
Expected value (expectation) of WOSA spectral estimator      291
Exponential distribution      233
Exponential rv      228
Extrapolation of a band-limited function      80
F-distribution      512
F-distribution, percentage points (special case)      501
F-test for periodicity      see "Tests for periodicity"
Fader      206
Farebrother, R.W.      494 549
Fast Fourier transform (FFT) algorithm      110 114 235 323 390 479 500 506 508 525
Fejer's kernel      95 198 200 203 260 271 324 475 484
FFT      see "Fast Fourier transform"
Figueiras-Vidal, A.R.      553
Filliben, J.      50 52
Filtering, terminology for      169
Filtering, theorem, analog      158
Filtering, theorem, digital      164
Filtering, time-invariant linear and convolutions      160
Filters for pilot analysis      185
Filters, acausal      170
Filters, band-pass      170
Filters, basic theory of LTI digital      164
Filters, cascaded      169
Filters, causal      170
Filters, example of acausal FIR      171
Filters, example of LTI digital      171
Filters, finite impulse response (FIR)      170
Filters, high-pass      170
Filters, high-pass by subtracting the output of a low-pass filter from its input      173
Filters, infinite impulse response (IIR)      170
Filters, linear time-invariant (LTI)      153
Filters, linear time-invariant (LTI), analog      155
Filters, linear time-invariant (LTI), digital      164 236
Filters, low-pass      169
Filters, low-pass, cutoff frequency      175
Filters, low-pass, design by least squares      176
Filters, low-pass, design using dpss      180
Filters, prewhitening      219 393
Filters, transformation or operator      154
Final prediction error (FPE)      436
Findley, D.F.      554
Finite impulse response (FIR) filter      170 443
FIR (finite impulse response) filter      170 443
First difference      51
First difference of the first difference      54
First difference, process      184
First harmonic      507
First-order autoregressive process      152
Fisher's test for simple periodicity      491 509 543
Fisher, R.A.      1 491 494 549
Flannery, B.P.      556
Folding frequency      98
Forward and backward least squares      427
Forward and backward prediction errors      414
Forward least squares      427
Forward prediction errors      400 438 440
Forward prediction errors, complex-valued process      451
Forward predictors      397 532
Fougere, P.F.      215 525—528 549—550
Fourier coefficient      59
Fourier frequencies      10 109 197 204 221 250 333 462 474—475 478 480 489
Fourier integral representation      65
Fourier series representation of a periodic function      59
Fourier synthesis      65
Fourier theory, continuous time/continuous frequency      64
Fourier theory, continuous time/discrete frequency      57
Fourier theory, discrete time/continuous frequency      87
Fourier theory, discrete time/discrete frequency      108
Fourier theory, summary      116
Fourier transform      65
Fourier transform of a convolution      81
Fourier transform of a discrete sequence with discrete frequencies      110
Fourier transform of a discrete time sequence      87
Fourier transform pairs      65 116—119
Fourier transform pairs, examples of      197 206—208 231 237—239 281—282 284—289 295 318—321 330 388
Fourier transform, fast      110
Fourier transform, sign of i convention      68
Fox, W.      303
FPE (final prediction error)      436
FPE order selection      436 520—521
FPE order selection, ocean wave data      439
Fractional difference process      190
Franke, J.      424 550
Fredholm integral equation, first kind      362
Fredholm integral equation, second kind      76 102
Frequency octave      259
Frequency response function      158 537
Frequency response function for Hilbert transform      538
Friedlander, B.      516—517 550
Frijling, D.J.      285 559
Fuller, W.A.      188 550
Fundamental Fourier frequency      333
fundamental frequency      507
Fundamental uncertainty relationship (variance-controlled width)      72
Gain function      158
Gamma function      493
Garbow, B.S.      558
Gauss — Legendre quadrature      385
Gaussian distribution      67 151 256 496
Gaussian distribution, complex      499
Gaussian distribution, Fourier transform of pdf      67
Gaussian kernel      82
Gaussian or normal process      38 410 429 449
Gaussian or normal process, complex      40
Gaussian sdf      151
Gaussian white noise      220 347
Gaussian-shaped, autocovariance function      151
Gaussian-shaped, spectral density function      151
Geckinli, N.C.      258 550
Generalized inverse      535—536
Geophysics      24
Gibbs phenomenon      93 177
Godolphin, E.J.      433 550
Gold, B.      96 169 182 556
Golden Gate Bridge      194—195
Golub, G.H.      453 533 548 550
Gould, A.      549
Gourlay, A.R.      382 550
Grandy, W.T., Jr.      548 550
Granger, C.W.J.      176 550
Graybill, F.A.      375 550
Greene, D.H.      34 550
Greenhall, C.A.      387—390 550
Grenander, U.      168 205 241 245 550
Grid size      224—225 229 231 233 299 324 479 481 506 525
Griffiths, P.      379 551
Group delay      158
Gruenbaum, F.A.      115—116 551
Hamming lag window      328
Hamming, R.W.      169 551
Hannan, E.J.      473 479 551
Hanning lag window      328 538
Hanning taper      210 293 325
Hanning taper, examples of use of      311—312 316—317
Hardin, J.C.      147 551
Harmonic analysis      456
Harmonic analysis of Willamette River data      504—505
Harmonic analysis, parametric approach      514
Harmonic analysis, singular value decomposition approach      531
Harmonic analysis, summary      539
Harmonic models for Willamette River data      508
Harmonic process, complex-valued      465 468 542
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