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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
Nonperiodic function, convolution theorem      117
Nonperiodic function, Fourier representation      117
Nonperiodic function, Parseval's theorem      117
Nonperiodic function, spectral properties      117
Nonstationary process example      53
Nonwhite noise      349 351 369—370
Normal (Gaussian) process      410 429 449
Normal equations      461
Normalization of the impulse response sequence      174
Normalized cumulative periodogram      234 511
Nowroozi, A.A.      491 555
Nuttall, A.H.      246 289 291 295 555
Nyquist frequency      98 127
Nyquist rate      147
Ocean noise data, description of      2
Ocean noise data, estimated spectrum for      21
Ocean noise data, lag 1 scatter plot for      4
Ocean noise data, periodicity testing with white noise      495
Ocean noise data, plot of      3
Ocean noise data, sample acs for      7
Ocean noise data, simulation of      17
Ocean noise data, testing for white noise      17
Ocean noise data, theoretical acs for      15
Ocean noise data, theoretical spectrum for      13 21
Ocean tide prediction      457
Ocean wave data      295
Ocean wave data, Burg autoregressive spectral estimator      439—440
Ocean wave data, direct spectral estimator      296 440
Ocean wave data, FPE order selection      439
Ocean wave data, lag window spectral estimator      301
Ocean wave data, multitaper spectral estimator      371 373
Ocean wave data, periodogram      296 298
Ocean wave data, plot of      295
Ocean wave data, prewhitening      439—441
Ocean wave data, Yule — Walker autoregressive spectral estimator      439—440
Oceanography      24
One-sided spectral density function      140
Ooe, M.      437 559
Oppenheim, A.V.      111 114 538 555
Orchestral music      69
Order of an autoregressive process      423
Order of Yule — Walker autoregressive spectral estimator      404
Order selection for autoregressive process      434
Order selection for autoregressive process, AIC method      436
Order selection for autoregressive process, direct spectral estimator method      437
Order selection for autoregressive process, FPE method      436 520—521
Order selection for autoregressive process, partial autocorrelation method      435
Orthogonal increments      129 150
Orthogonal process      129 168
Orthogonal tapers      334
Orthogonality principle      398—402 454
Orthogonality relationships      18 28 221
Orthonormal basis      160 362
Orthonormal basis, nonuniqueness of      161
Orthonormality      384 388—389 534
Oscilloscope      30
Outliers      218 298
Oversmoothing      84
Oxygen isotope ratios      333
PACs      see "Partial autocorrelation sequence"
Pagano, M.      433 445 480 555
Papoulis lag window      266—267 269 271 445
Papoulis, A.      30 136 266 397 403 410 530 537 555
Parametric approach to harmonic analysis      514
Parametric approach to harmonic analysis, AR(2) example      517
Parametric approach to harmonic analysis, AR(24) example      519
Parametric approach to harmonic analysis, problems with      525
Parametric approach to harmonic analysis, Willamette River data      520
Parametric estimation      22
Parametric spectral estimation      391 442 453
Parametric spectral estimation, summary      451
Parekh, A.      551
Park, J.      333 500 554—556
Parlett, B.N.      382 384 556
Parseval's theorem      59 66 89 101 111 116—119
Parseval's theorem, applications of      62 69 74 208 242 248 279 282 324 364
Parseval's theorem, multitaper spectral estimator and      371 377
Parseval's theorem, two function version      120 125
Partial autocorrelation coefficient      402 414 417
Partial autocorrelation sequence (PACS)      409—410 435
Partial autocorrelation sequence (pacs), complex-valued process      451
Parzen lag window      265—266 268—271 275 289 302—303 306 308 315 328 372 442 445 470—471
Parzen smoothing window      266 271
Parzen, E.      243 265 268 423 549 556
Pdf (probability density function)      54 228
Peak shifting      526—527
Peak shifting and splitting with Burg's algorithm      526
Peak shifting and splitting, 'analytic' series      530
Peak shifting and splitting, Burg's algorithm      531
Peak shifting and splitting, multiple sinusoids      531
Peak shifting and splitting, Yule — Walker approach      528—530
Pearson product moment correlation coefficient      5
Percentage of block overlap      293
Percentage points of chi-square distribution      256
Percival, D.B.      528 547
periodic extension      112
Periodic function      58
Periodic function, convolution theorem      117
Periodic function, Fourier representation      116
Periodic function, Parseval's theorem      116
Periodic function, spectral properties      117
periodicity      52
Periodicity, compound      491—492
Periodicity, simple      491—492
Periodicity, testing with colored noise      496
Periodicity, testing with colored noise, Thomson's F-test      300 499 512 544
Periodicity, testing with white noise      489 543
Periodicity, testing with white noise, Fisher's test for simple periodicity      491 495 509 543
Periodicity, testing with white noise, ocean noise data      495
Periodicity, testing with white noise, Schuster's test for simple periodicity      490
Periodicity, testing with white noise, Siegel's test for compound perodicity      492 495 543
Periodogram      138 196—197 221 318 324 452 465 473 475 490
Periodogram at Fourier frequencies      204
Periodogram at zero frequency      204
Periodogram of a centered time series      324
Periodogram, AR(2) data      234 308
Periodogram, AR(4) data      313
Periodogram, asymptotic unbiasedness of      199
Periodogram, bias of      201—203
Periodogram, complex-valued process      317
Periodogram, covariances of      222—223
Periodogram, distribution of      221—222 319
Periodogram, expected value of      198 319 324
Periodogram, ice profile data      305
Periodogram, inconsistency of      224—225
Periodogram, modified      207
Periodogram, ocean wave data      296—298
Periodogram, rescaled      491 495
Periodogram, spectral window for      319
Periodogram, spurious peaks      478
Periodogram, sum over Fourier frequencies (N even)      545
Periodogram, sum over Fourier frequencies (N odd)      545
Periodogram, truncated      327
Periodogram, variance of      222 319
Periodogram, white noise      348
Periodogram, Willamette River data      505—506
Phase function      158
Phase shift function      158
Phase-shifted Fourier transform      361
Phases as independent random variables      47 457 459
Phases, nonuniformly distributed      54
Pignari, S.      523 556
Pilot analysis, filters for      185
Pisarenko, V.F.      516 556
Poisson's formula      100
Pollak, H.O.      80 557
Polynomial regression model      471
Poor, H.V.      553
Positive, definite      37 195 353
Positive, semidefinite      37 193 195 352—353
Postcoloring      438 442
Power of a nonperiodic function      66
Power of a periodic function      59
Power spectral density function (psdf)      134 138
Prediction errors, backward      400
Prediction errors, forward      400 438 440
Prediction errors, forward and backward      414
Prediction errors, variance      422
Prescott, P.      48 459 560
Press, H.      218 556
Press, W.H.      379—380 385—386 453 480 493 538 556
Prewhitening      203 218 317 329 331 343 393 432 434 437 439—440 442—443 453
Prewhitening, filter      219 393 432 434 437
Prewhitening, ocean wave data      439—441
Priestley, M.B.      30 127 130 134—136 139—140 243—244 258—259 266 273 276 326 392 410 421 471 484 489 494 556
Principle of maximum entropy      393 421 423—424
Probability density function (pdf)      54 228
Probability of an event      33
Projections      376
Prolate spheroidal wave function (pswf)      77 384
psdf (power spectral density function)      134 138
Pseudo-AR process      515—516 531
Pseudo-AR process, complex      531
pswf (prolate spheroidal wave function)      77 384
Pure parametric approach to spectral estimation      432 434 437 453
Purely continuous, spectrum      141 187 189 193
Purely continuous, stationary process      484
Purely discrete spectrum      141 456—457
Quadratic spectral estimator      351
Quadratic spectral estimator, bias of      359
Quadratic spectral estimator, expected value of      353 355
Quadratic spectral estimator, relationship to direct spectral estimator      353
Quadratic spectral estimator, spectral window      354
Quadratic spectral estimator, variance of      359
Quadratic spectral estimator, weight matrix for      359
Quadratic taper      238
Quadratic window      238
Quadratic window, estimator      242
Rabiner, L.R.      96 169 182 393 556
Radar clutter      151
Radoski, H.R.      550
Rainfall      25
Ramsey, F.L.      409 556
Random amplitudes      131
Random phases      131
Random variable      5 31
Randomly phased sinusoid      515 528
Randomly phased sinusoid, covariance of      515 545
Randomly phased sinusoid, plus white noise      516
Rank of matrix      534—535
Rayleigh's theorem      59
Real-valued continuous parameter stochastic process      32
Real-valued discrete parameter stochastic process      32
Real-valued stationary process      35
realizations      5 31
Reciprocity relationships, equivalent width      70
Reciprocity relationships, fundamental uncertainty relationship      72
Reciprocity relationships, similarity theorem      70
Rectangular kernel      86
Rectangular taper      207—209 326 472 486
Reduced likelihood      431
Reflection coefficient sequence      409
Regularization      365
Reid, J.S.      445 556
Rejection filtration      219
Rescaled periodogram      491 495
Reshaped lag window      246 269—270
Reshaped spectrum      500 504
Reshaped spectrum, Willamette River data      513
Residual process      503
resistor      52
Resolution      332 354
Resolution, bandwidth      335 354 371—372 374
Resolution, loss      90
Restoration of power      216
Reversibility of time series      434
Rice, J.A.      478 556
Rice, S.O.      278 556
Richardson, G.A.      558
Riemann integral      34 250
Riemann — Stieltjes integral      33 34 129
Riemann — Stieltjes integral, ordinary      150
Riemann — Stieltjes integral, stochastic      150
Rife, D.C.      488 503—504 557
Ringing      218 298
Ripples      208 273 315
Roberts, D.E.      256 547
Robinson, L.      549
Rolloff of sidelobes      271
Rolloff of smoothing window      271
Rolloff of spectral window      271
Rosenblatt, M.      168 245 410 436 478 547 550 556—557
Rotation of the earth      333
Rule-of-thumb for significance levels      513
Samarov, A.      190 557
Sample autocorrelation      5 8 13
Sample autocorrelation sequence (sample acs)      5
Sample autocorrelation, correlation of      8
Sample autocorrelation, standard deviation of      8
Sample autocovariance sequence (sample acvs)      276
Sample mean      188 204 233 294
Sampled signal      87
Sampling and aliasing      144
Santamaria-Perez, M.E.      553
Sarkar, T.K.      535 551 559
Satorius, E.H.      514 557
Scarano, G.      151 551
Schafer, R.W.      111 114 393 538 555—556
Scharf, L.L.      333 555 559
Scheffe, H.      447 557
Scher, M.S.      558
Schur matrix      433
Schuster's test for simple periodicity      490
Schuster, A.      490 557
Schwarz inequality      68—69 74
SDF      see "Spectral density function"
Sea levels      468
Seasonality      52
Semivariance      465 498
Sequency (Walsh functions)      161
Sequency-limited and time-limited      164
Shading sequence      206
Shannon number      79 107 334 350—351 360—361
Shimshoni, M.      491 494 509 557
Sidelobes      91
Sidelobes of Fejer's kernel      203 478 486
Sidelobes of spectral window      210 342
Siegel's test for compound periodicity      492 495 543
Siegel, A.F.      491—492 494 557
Signal-to-noise ratio      477 483 494 523 529
Similarity theorem      70 123
Simple periodicity      491—492 543
Simulated time series      11
Sine function      76 526
Single-sided spectral density function      140
Singleton, R.C.      114 557
Singular value decomposition (SVD)      533—535
Singular value decomposition (SVD) and short time series      537
Singular value decomposition (SVD), approach to harmonic analysis      531
Singular value decomposition (SVD), Willamette River data      537
Singular values      534
Singular vectors      534
Sinusoid, deterministic      514 525
Sinusoid, randomly phased      515 528
Sinusoidal amplitude estimator, approximate conditional least squares      502 509 511
Sinusoidal amplitude estimator, approximate least squares (real)      464 476 541
Sinusoidal amplitude estimator, exact conditional least squares      502
Sinusoidal amplitude estimator, exact least squares (complex)      466 543
Sinusoidal amplitude estimator, exact least squares (real)      463 541
Sinusoidal amplitude estimator, exact unconditional least squares      502
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