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