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| Авторизация |
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| Percival D., Walden A. — Spectral Analysis for Physical Applications |
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| Предметный указатель |
Sinusoidal amplitude estimator, multitaper (complex) 499 504 513
Sinusoidal frequency estimator 473 475
Sinusoidal frequency estimator, convergence of (colored noise) 479
Sinusoidal frequency estimator, effect of grid size 481
Sinusoidal frequency estimator, effect of series length 484
Sinusoidal frequency estimator, expected value using periodogram peak 477
Sinusoidal frequency estimator, location of AR sdf peaks 519 524
Sinusoidal frequency estimator, location of periodogram peaks 479 488—489
Sinusoidal frequency estimator, parametric approach 514
Sinusoidal frequency estimator, periodogram at Fourier frequencies (complex) 474 543
Sinusoidal frequency estimator, periodogram at Fourier frequencies (real) 473 541
Sinusoidal frequency estimator, periodogram at general frequencies 475 541
Sinusoidal frequency estimator, tapering 486 489 542
Sinusoidal frequency estimator, three sinusoid example with noise 481
Sinusoidal frequency estimator, three sinusoid example, noise-free 480
Sinusoidal frequency estimator, variance using periodogram peak 477 545
Sinusoidal variations 393 443
Sinusoids, decaying 500
Sinusoids, sum of 10 28 46
Sjoholm, P.F. 280 283 557
Slepian sequence 181 see
Slepian, D. 69 70 73 75 79—80 101 103—104 123 363 379 385—386 389 557
Sloane, E.A. 216 348 558
Smith, B.T. 379 387 558
Smith, C.R. 548 550
Smith, W.L. 546
Smoothed periodogram estimator 242
Smoothing window 238 240 322
Smoothing window types, Bartlett 260
Smoothing window types, Daniell 263
Smoothing window types, modified Daniell 267
Smoothing window types, Papoulis 266
Smoothing window types, Parzen 265
Smoothing window types, rectangular 263
Smoothing window, bandwidth 241—242 273 276 300 306 311 317 470 472
Smoothing window, examples 259
Smoothing window, leakage 259 272 300 303 306 442
Smoothing, direct spectral estimator 235
Smoothing, kernel 82
Smoothing, log spectral density estimator 280 311
Smoothing, parameter 82 244 471
Spann, M. 116 561
Spectral analysis 10
Spectral analysis, deterministic 56
Spectral analysis, maximum entropy method 215
Spectral analysis, multitaper approach 215 331
Spectral analysis, uses of 23
Spectral bandwidth 274
Spectral bandwidth, estimation of 277
Spectral density function (sdf) 132 187
Spectral density function (sdf) and linear filters 158
Spectral density function (sdf) of AR process of order p 168 392 446
Spectral density function (sdf) of ARM A process of order (p,q) 168 184
Spectral density function (sdf) of band-limited white noise 357
Spectral density function (sdf) of first difference process 184
Spectral density function (sdf) of MA process of order q 151 167
Spectral density function (sdf) versus autocovariance sequences 147
Spectral density function (sdf), alternative definitions 136
Spectral density function (sdf), basic properties 138
Spectral density function (sdf), confidence intervals 255—256 299 302 445
Spectral density function (sdf), Gaussian-shaped 151
Spectral density function (sdf), Lorenzian 152
Spectral density function (sdf), one-sided 140
Spectral density function (sdf), two-sided 140
Spectral density function (sdf), unimodal 277
Spectral distribution function 139
Spectral estimation, negative estimates 269
Spectral estimation, nonparametric 187
Spectral estimation, parametric 391 442
Spectral estimation, pure parametric approach 453
Spectral estimation, Yule — Walker 396
Spectral estimator, Grenander — Rosenblatt type 242
Spectral lines 489
Spectral lines, splitting of 525—526 528
Spectral representation of stationary process 127 130
Spectral representation of stationary process, discrete spectrum 467 540
Spectral representation of stationary process, mixed spectrum 467 540
Spectral representation, theorem 10 127 361 467
Spectral representation, theorem for complex-valued stationary process 135
Spectral representation, theorem for continuous parameter stationary process 134 157
Spectral representation, theorem for discrete parameter stationary process 130
Spectral reshaping 500 504 513
Spectral window 207 209—212 244 486
Spectral window type, Bartlett 260
Spectral window type, Daniell 263
Spectral window type, direct spectral estimator 320
Spectral window type, kth order dpss 337 339 342
Spectral window type, lag window spectral estimator 321
Spectral window type, modified Daniell 267
Spectral window type, multitaper spectral estimator 334 340—342
Spectral window type, Papoulis 266
Spectral window type, Parzen 265
Spectral window type, periodogram 319
Spectral window type, quadratic spectral estimator 354
Spectral window type, rectangular 263
Spectral window, examples 259
Spectral window, rolloff rate 271
Spectrograph estimator 242
Spectrum 10—11
Spectrum, analyzers 294—295
Spectrum, classification 141
Spectrum, constant 16
Spectrum, discrete 141 456 460 540
Spectrum, estimated 19
Spectrum, high frequency 15
Spectrum, interpretation via band-pass filtering 170
Spectrum, line 15 141 456
Spectrum, low frequency 13
Spectrum, mixed 141 461 470 472 540
Spectrum, purely continuous 141
Spectrum, purely discrete 141 456—457
Spectrum, theoretical 19
Spencer-Smith, J.L. 44 443 558
Spinning rotor 49
Spliid, H. 52 549
Spontaneous line splitting see "Spectral lines"
Spurious spectral peaks 537
Square integrability 58 64—65
St. Paul temperature data, description of 8
St. Paul temperature data, lag k scatter plots for 9
St. Paul temperature data, plot of 9
Standard frequencies 109 462
Stationarity 38
Stationarity, autoregressive process 392 414
Stationarity, autoregressive process, necessary and sufficient condition 168
Stationarity, moving average process 43
Stationarity, second-order/weak/covariance 35
Stationarity, strict/complete/strong 35
Stationary process 6 10 30
Stationary process and modeling data 49
Stegen, G.R. 514 525—527 549
Stegun, I.A. 385 546
Stephens, M.A. 234 558
Stevens, W.L. 492 558
Stochastic continuity 135 140
Stochastic process 30
Stoffer, D.S. 164 558
Storm surges 472
Structured covariance matrices 333
Sum of sinusoids 10 28 46
SVD see "Singular value decomposition"
Swanepoel, J.W.H. 445 558
Sydnor, R.L. 546
Szegoe — Kolmogorov theorem 421
Szegoe, G. 205 550
Tables, Burg's algorithm and sinusoid estimation 527
Tables, characteristics of AR sdf's for Willamette River data 523
Tables, coefficients for generating trig prolates 390
Tables, critical values for Siegel's test 493
Tables, eigenvalues and quadruple precision 382
| Tables, lack of precision in eigenvalue computations 380
Tables, percentage points for chi-square distribution 256
Tables, properties of lag windows 269
Tables, true and estimated sinusoidal frequencies 486
Tables, variance inflation factor for tapers 248
Tapering 203 206 215 317 486 542
Tapering and Yule — Walker autoregressive spectral estimator 396 405
Tapering, multiple 331 349
Tapers and rolloff rate 271
Tapers type, cosine 209—210
Tapers type, dpss 211—212 227 297 313 334 336 338 439 486 497 507 520
Tapers type, Hanning 210 317 325 487
Tapers type, linear 206
Tapers type, quadratic 238
Tapers type, rectangular 209 486
Tapers, orthogonal set 334
Tapers, variance inflation factor 248
Taqqu, M.S. 190 557
Taylor, A.E. 34 558
Terrestrial free oscillations 333
Tests for periodicity, colored noise 496
Tests for periodicity, multitaper approach 496
Tests for periodicity, Thomson's F-test 499 512 544
Tests for periodicity, white noise 489 543
Teukolsky, S.A. 556
Textile slivers 44 443
Theoretical autocorrelation 6 13
Thermal noise 24
Therrien, C.W. 412 454 558
Thomson, D.J. 199 218 230—231 292 294 298 331—333 335 351 360—362 365—366 370 377 384—385 439 459 490 496 500—501 512 548 553—555 558
Tiao, G.C. 559
Tidal analysis 52
Tidal frequencies 470
Time reversed process 450
Time reversed process, complex conjugate of 450
Time-limited signals 69
Titchmarsh, E.C. 93 141 559
Tjostheim, D. 414 433 554
Todd, H.A.C. 44 443 558
Toeplitz, matrix 38 181 382 403 408 430 433
Toeplitz, matrix, Hermitian 40
Toeplitz, system of equations 396 406
Toman, K. 525 559
Tong, H. 516—517 559
Trace of a matrix 354 356 358 376
Tradeoff between bias and variance 96
Tradeoff between fidelity and resolution 96
Transfer function 158 166 273 448 537
Transfer function, Hilbert transform 538
Trend 52 176
Trig prolates 388
Trigonometric polynomial 387 475
Truncated periodogram 327 445
Tseng, F.I. 520 559
Tufts, D.W. 532 535—537 559
Tugnait, J.K. 517 559
Tukey, J.W. 206 218—219 227 327 547 556 559
Tukey, P.A. 548
Twin peaks 91—92 213 274 313 315—317 404
Two degrees of freedom estimate 21
Two-sided spectral density function 140
Ulrych, T.J. 46 435 437 514 516 526—527 559
Uncorrelated random amplitudes 48
Undersmoothing 84
Unit circle 392
Units for sdf 306
Unweighted least squares 471
Unwin, J.M. 433 550
Van Loan, C.F. 453 533 550
Van Schooneveld, C. 285 559
Van Veen, B.D. 332—333 554 559
Van Wyk, J.W.J. 445 558
Variance 6 11 33
Variance of a linear combination of random variables 55
Variance of direct spectral estimator 223 320
Variance of lag window spectral estimator 247 251 321
Variance of multitaper spectral estimator 334 343 350
Variance of periodogram 222 319
Variance of quadratic spectral estimator 359
Variance of WOSA spectral estimator 292
Variance spectrum of a harmonic process 128
Variance, inflation factor due to tapering 248
Variance, normalization 216
Variance-controlled width 121
Variance-covariance matrix 38
Vernon, F.L., III 556
Vessot, R.F.C. 546
Vetterling, W.T. 556
Vincent, G.A. 488 557
Wahba's automatic smoothing criterion 311 317
Wahba, G. 280 560
Wald, A. 446 554
Walden, A.T. 48 229 251 253 268 272 277 280 333 344 386 459 471 493 547 560
Walker, A.M. 477 516 560
Walker, J. 25 560
Walsh functions 161
Warburg, H.D. 457 549
Watson, G.A. 382 550
Watts, D.G. 185 194 273 551
Weight associated with kth eigenspectrum 368
Weighted covariance estimator 242
Weighted least squares 471
Weighted overlapped segment averaging spectral estimator see "WOSA spectral estimator"
Weiner, D.D. 559
Weinstein, E. 445 449 548
Weiss, G. 434 560
Welch's overlapped segment averaging spectral estimator see "WOSA spectral estimator"
Welch, P.D. 289 292 560
White noise 16—17 28 41—42
White noise and estimation of complex exponentials 504
White noise, added to randomly phased sinusoids 144 477—478 516—517
White noise, band-limited 357
White noise, complex-valued 465 532
White noise, direct spectral estimator 208 348
White noise, estimator of variance 502
White noise, Gaussian 490
White noise, multitapering 347—351
White noise, periodogram 201—202 220—222 224—225 231 348 481—484
White noise, sdf for 139
White noise, tapering 216
White noise, test for 233
White noise, variance estimator, approximate conditional least squares 502 509 511
White noise, variance estimator, exact conditional least squares 502
White noise, variance estimator, exact least squares, complex 466
White noise, variance estimator, exact least squares, real 464
White noise, variance estimator, exact unconditional least squares 502
White noise, variance estimator, multitaper 504
White, R.E. 251 272 277 280 560
Whittle, P. 477 494 560
Wiener — Khintchine theorem 140
Wiener, N. 94 560
Willamette River data, Burg autoregressive spectral estimator 520 522
Willamette River data, cumulative periodogram test of residuals 510—511
Willamette River data, description of 1
Willamette River data, direct spectral estimator of 505 507
Willamette River data, estimated spectrum for 20
Willamette River data, FPE order selection 520—521
Willamette River data, harmonic analysis of 504—505
Willamette River data, integrated autoregressive spectrum 522
Willamette River data, lag 1 scatter plot for 4
Willamette River data, multitaper spectral estimator 513
Willamette River data, parametric approach to harmonic analysis 520
Willamette River data, periodogram 505—506 508—511
Willamette River data, plot of 'analytic' series for 539
Willamette River data, plot of complex roots for 539
Willamette River data, plot of fitted model 508 510
Willamette River data, plot of residuals 508 510—511
Willamette River data, plot of series 2 504—505
Willamette River data, reshaped spectrum 512—513
Willamette River data, sample acs for 6
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