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| Farhang-Boroujeny B. — Adaptive filters: theory and applications |
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| Предметный указатель |
Normalized least-mean-square (NLMS) algorithm, geometrical interpretation of 174
Normalized least-mean-square (NLMS) algorithm, Nitzberg's interpretation of 172—173 194
Normalized least-mean-square (NLMS) algorithm, summary 175
Observation vector 89
Omni-directional antenna 78 166
One-step forward prediction 357
Optimum linear discrete-time fillers see "Linear prediction" "Wiener
Order of N complexity transforms see "Fast recursive least-squares algorithms" "Sliding
Order-update equations 357 364 368
Orthogonal coefficient vectors 219
Orthogonal complementary projection operator 419
Orthogonal transforms 202
Orthogonal transforms, band-partitioning property of 204—205 224
Orthogonal transforms, orthogonalization properly of 205—208
Orthogonal, random variables 57
Orthogonality of backward prediction errors 363 445
Orthogonality principle see "Principle of orthogonality"
Orthonormal matrix 479
Overlap-add method 254
Overlap-save method 254
Overlap-save method, matrix formulation of 256—257
Oversampling 345
Parallel processing 247
Parallel processor 748
Parametric modelling of random processes autoregressive (AR) 15 387 see
Parametric modelling of random processes autoregressive (AR), autoregressive moving average (ARMA) 15
Parametric modelling of random processes autoregressive (AR), moving average (MA) 15
Parametric spectral analysis 17 387
Parseval's relation 34 97 220
Partial correlation (PARCOR) coefficients 367 445
Partial response signalling 13
Partitioned fast block LMS (PFBLMS), algorithm 265—278
Partitioned fast block LMS (PFBLMS), analysis 268—270
Partitioned fast block LMS (PFBLMS), block diagrams 267 271
Partitioned fast block LMS (PFBLMS), computational complexity 273—274
Partitioned fast block LMS (PFBLMS), computational complexity, example 274
Partitioned fast block LMS (PFBLMS), computer simulations 275—278
Partitioned fast block LMS (PFBLMS), constrained on rotational basis 275
Partitioned fast block LMS (PFBLMS), constrained versus unconstrained 269 270
Partitioned fast block LMS (PFBLMS), frequency bin filters 268
Partitioned fast block LMS (PFBLMS), learning curves 277 278
Partitioned fast block LMS (PFBLMS), misadjustment equations 273
Partitioned fast block LMS (PFBLMS), modified constrained PFBLMS algorithm 275
Partitioned fast block LMS (PFBLMS), overlapping of partitions 269
Partitioned fast block LMS (PFBLMS), summary 272
Performance function, based on deterministic framework 2
Performance function, based on statistical framework 2
Performance function, canonical form 106
Performance function, normalized form 59
Performance function, unconstrained Wiener filter, of 63—64
Performance indices 215
Performance surface, contour plots 105
Performance surface, defined 89
Performance surface, eccentricity 108 110 211 213
Performance surface, eigenvalue spread effect 108
Performance surface, examples 56 109
Performance surface, extension to complex-valued case 112—113
Performance surface, hyperparabola shape 107
Performance surface, transversal Wiener filters, of 104—113
Phase shift keying (PSK) 9 59
Positive definite correlation matrix 90
Power inversion formula 78
Power inversion formula, example of 78—81
Power line interference cancellation 18
Power normalization 201 206
Power spectral density 40—42
Power spectral density, defined 40
Power spectral density, estimation 17 387
Power spectral density, interpretation 42 44
Power spectral density, properties 42
Power spectral density, relationship with autocorrelation coefficients 41 377
Power spectral density, relationship with linear predictor coefficients 377
Power spectral density, transmission of a stationary process through a linear filter 44
Power spectrum see "Power spectral density"
Prediction applications 17—20
Prediction errors, properties of 362—364
Prediction-error filters 361—362 see
Prewindowing of input data 446
Primary input 21 76
Principle of correlation cancellation 70
Principle of orthogonality, complex-valued signals, for the case of 61
Principle of orthogonality, corollary to 57
Principle of orthogonality, least-squares estimation, in 416—417
Principle of orthogonality, linear predictors, in 363
Principle of orthogonality, unconstrained Wiener fillers, in 66
Principle of orthogonality, Wiener filters, in 56—57
Processing delay (latency) 265 274 302 305 306 319
Projection operator 418—419
Prototype filler 294 311
Pulse-code modulation, adaptive differential 20
Pulse-spreading effect 12 see
QR-decomposition-based recursive least-squares (QRD-RLS) 8
QRD-RLS algorithm 8
Quadrature-amplitude modulation (QAM) 9 59 178
Quasi LMS-Newton algorithm 210
Raised cosine pulse 490
Random process see "Stochastic processes"
Random variables, inner product 58
Random variables, orthogonality 57
Random variables, projection 58
Random variables, subspaces 58
Random walk 491
Random walk, approximate realization of 491
Real DFT 224
Real DFT, non-recursive sliding realization of 233
Receiver noise 12
Recursive algorithms see "Names of specific algorithms"
Recursive least-squares (RLS) algorithms see also "Least-squares lattice"
Recursive least-squares (RLS) algorithms, a priori and a posteriori estimation errors 446
Recursive least-squares (RLS) algorithms, augmented normal equations 448
Recursive least-squares (RLS) algorithms, classification 8
Recursive least-squares (RLS) algorithms, computational complexity 461
Recursive least-squares (RLS) algorithms, conversion factor 447 450—452
Recursive least-squares (RLS) algorithms, conversion factor, update recursion 453
Recursive least-squares (RLS) algorithms, cross-correlations 447 453—456
Recursive least-squares (RLS) algorithms, cross-correlations, update recursions 456
Recursive least-squares (RLS) algorithms, least-squares error sums 447
Recursive least-squares (RLS) algorithms, least-squares error sums, update recursions 450
Recursive least-squares (RLS) algorithms, notations and preliminaries 446—449
Recursive least-squares (RLS) algorithms, numerical stability 439 458
Recursive least-squares (RLS) algorithms, prewindowing of input data 446
Recursive least-squares (RLS) algorithms, QR-decomposition RLS 8 see
Recursive least-squares (RLS) algorithms, Recursive least-squares estimation see "Recursive least-squares algorithms" "Recursive "Fast
Recursive least-squares (RLS) algorithms, Recursive least-squares lattice (RLSL) algorithms 8 439 446—460
Recursive least-squares (RLS) algorithms, RLSL algorithm using a posteriori errors 456—458
Recursive least-squares (RLS) algorithms, RLSL algorithm using a posteriori errors, summary 457
Recursive least-squares (RLS) algorithms, RLSL algorithm with error feedback 458—460
Recursive least-squares (RLS) algorithms, RLSL algorithm with error feedback, summary 459
Reference input 21 76
Region of convergence 29
Region of convergence, stable systems, of 35
Regressor tap-weight vector 425
Repeated eigenvalues 90
Rescue variable 465 466
Residue theorem 33
RLS algorithm see "Standard recursive least-squares algorithms"
Roll off factor 311
Rotation of the coordinate axes 213
Rotation of the performance surface 213
Round-off error 229 236 425 460
Self-tuning regulator (STR) 10
Sign algorithm 169
Sign-sign algorithm 169
Signal-to-noise power spectral density ratio 69
Signed-regressor algorithm 169
Simplified LMS algorithms 169—172
Simplified LMS algorithms, computer simulations 170
Simplified LMS algorithms, convergence behaviour 171 193—194
Simplified LMS algorithms, sign algorithm 169
Simplified LMS algorithms, sign-sign algorithm 169
| Simplified LMS algorithms, signed-regressor algorithm 169
Sine wave plus noise, correlation matrix 101
Sinusoidal interference cancellation 18 335
Sliding transforms 225—237
Sliding transforms, Braun's algorithm as a sliding DFT 230—233
Sliding transforms, complexity comparisons 237
Sliding transforms, frequency sampling filters 226—227
Sliding transforms, frequency sampling filters, common properly of 230
Sliding transforms, frequency sampling filters, transfer functions of 227
Sliding transforms, recursive realization of 227—230
Sliding transforms, recursive realization of, stabilization 230
Sliding transforms, recursive realization of, stabilizing factor 236
Sliding transforms, round-off error 229 236
Sliding transforms, stability 229
Software implementation 235 320 388
Source coders see "Speech coding"
Spectral estimation 15
Spectral estimation, parametric and non-parametric 17
Spectrum see "Power spectral density"
Spectrum analysis 17 387
Speech coding/processing 18—20 357
Speech coding/processing, adaptive DPCM (ADPCM) 20
Speech coding/processing, ADPCM encoder-decoder 20
Speech coding/processing, differential PCM (DPCM) 20
Speech coding/processing, ITU recommendation G 726 20
Speech coding/processing, linear prediction and 357
Speech coding/processing, linear predictive coding 19
Speech coding/processing, pilch period 19
Speech coding/processing, pulse code modulation (PCM) 19
Speech coding/processing, voiced and unvoiced sounds 19
Speech coding/processing, waveform coding 19—20
Square-root of a matrix 113
Stability see "Names of specific algorithms"
Standard recursive least-squares (RLS) algorithms 8 419—425 see
Standard recursive least-squares (RLS) algorithms, a posteriori and a priori estimation errors 422 432
Standard recursive least-squares (RLS) algorithms, average tap-weight behaviour 425—426
Standard recursive least-squares (RLS) algorithms, comparison with the LMS algorithm 452
Standard recursive least-squares (RLS) algorithms, computational complexity and alternate implementation of 424
Standard recursive least-squares (RLS) algorithms, computer simulations 432—433
Standard recursive least-squares (RLS) algorithms, convergence behaviour 425—434
Standard recursive least-squares (RLS) algorithms, derivation of RLS recursions 419—422
Standard recursive least-squares (RLS) algorithms, effect of initialization on the steady state performance of 422
Standard recursive least-squares (RLS) algorithms, eigenvalue spread and 430 432
Standard recursive least-squares (RLS) algorithms, excess mean-square error 430
Standard recursive least-squares (RLS) algorithms, fine-tuning process 431
Standard recursive least-squares (RLS) algorithms, forgetting factor 419
Standard recursive least-squares (RLS) algorithms, forgetting factor, measure of memory, as a 420
Standard recursive least-squares (RLS) algorithms, gain vector 421 422
Standard recursive least-squares (RLS) algorithms, independence assumption 428
Standard recursive least-squares (RLS) algorithms, initialization of 422—423
Standard recursive least-squares (RLS) algorithms, learning curve 427—430
Standard recursive least-squares (RLS) algorithms, LMS-Newton algorithm and 430 494
Standard recursive least-squares (RLS) algorithms, misadjustment 430
Standard recursive least-squares (RLS) algorithms, one iteration of 422
Standard recursive least-squares (RLS) algorithms, rank deficiency problem in 432
Standard recursive least-squares (RLS) algorithms, round-off error accumulation in 424
Standard recursive least-squares (RLS) algorithms, stable implementation of 424
Standard recursive least-squares (RLS) algorithms, summary 423
Standard recursive least-squares (RLS) algorithms, tap-weight misalignment 435
Standard recursive least-squares (RLS) algorithms, time constant 429
Standard recursive least-squares (RLS) algorithms, tracking behaviour 420 473 479 481 482
Standard recursive least-squares (RLS) algorithms, transient behaviour of 431—434
Standard recursive least-squares (RLS) algorithms, variable forgetting factor, with 494—496
Standard recursive least-squares (RLS) algorithms, variable forgetting factor, with, summary 495
Standard recursive least-squares (RLS) algorithms, weight-error correlation matrix 426—427
Standard recursive least-squares (RLS) algorithms, weighting factor 419
Stationary processes see "Stochastic processes"
Steepest descent, method of 120—131
Steepest descent, method of, bounds on the step-size parameter 123
Steepest descent, method of, effect of eigenvalue spread 130—131
Steepest descent, method of, geometrical ratio factors 130
Steepest descent, method of, learning curve 127—130
Steepest descent, method of, learning curve, numerical example 128—130
Steepest descent, method of, modes or convergence 123 125 128
Steepest descent, method of, optimum value of step-size parameter 131
Steepest descent, method of, overdamped and underdamped 123 124
Steepest descent, method of, power spectral density effect 131
Steepest descent, method of, search steps 121
Steepest descent, method of, stability 123
Steepest descent, method of, step-size parameter 122
Steepest descent, method of, time constants 128
Steepest descent, method of, trajectories 127
Steepest descent, method of, transient behaviour of mean-square error 125
Steepest descent, method of, transient behaviour of tap-weight vector 125
Steepest descent, method of, transient behaviour of tap-weight vector, numerical example 125—127
Step-normalization 208 225 261
Stochastic gradient vector 141 263 326 487
Stochastic gradient-based algorithms see "Least-mean-square algorithm"
Stochastic processes 36—46
Stochastic processes, ensemble averages 37
Stochastic processes, ergodicity 46
Stochastic processes, jointly stationary 38
Stochastic processes, mutually exclusive spectral bands, with 205
Stochastic processes, power spectral density 40—42
Stochastic processes, response of linear systems to 42—45
Stochastic processes, stationary in the strict sense 37
Stochastic processes, stationary in the wide sense 37
Stochastic processes, stochastic averages 37—39
Stochastic processes, z-transform representations 39—40
Subband adaptive filters 9 293 see "Synthesis
Subband adaptive filters, application to acoustic echo cancellation 317—319
Subband adaptive filters, comparison with the FBLMS algorithm 319—320
Subband adaptive filters, computational complexity 306—307
Subband adaptive filters, decimal ion factor and aliasing 307—309 315 317
Subband adaptive filters, delay (latency) 302 305 306
Subband adaptive filters, misadjustment 309
Subband adaptive filters, selection of analysis and synthesis filters 303—306
Subband adaptive filters, slow convergence, problem of 304
Subband adaptive filters, stability 303
Subband adaptive filters, structures 302—304
Subband adaptive filters, structures, synthesis dependent 304
Subband adaptive filters, structures, synthesis independent 303
Superposition 2
System function 34—36
System identification 10
System modelling 10—11 157—159 324
Tap inputs 3
Tap weights 3
Tap weights perturbation 152 186 194 285 309
Tap-input vector 51
Tap-weight misalignment 196 435
Tap-weight vector 51
Tapped-delay line filter see "Transversal filter"
Target response 13 344
Time and ensemble averages 46 49
Time constants see "Names of specific algorithms"
Trace, of matrix 93 154
Tracking 11 460 471
Tracking, comparison of adaptive algorithms 479—485
Tracking, convergence and 471 496
Tracking, formulation of 471—472
Tracking, independence assumption 472
Tracking, multivariate random-walk process 472
Tracking, noise and lag misadjustments 477
Tracking, optimum step-size parameters for 477—479
Tracking, process noise vector 472
Tracking, unified study 472 see
Training mode 11 13
Transfer function, backward prediction-error filters 373
Transfer function, definition 2 34
Transfer function, forward prediction-error filters 373
Transfer function, I1R fine enhancer 334
Transform domain adaptive fillers 201 293 see
Transform domain adaptive fillers, lattice predictors and 370
Transform domain adaptive fillers, minimum mean-square error 203
Transform domain adaptive fillers, overview 202—204
Transform domain adaptive fillers, Wiener — Hopf equation 203
Transform domain LMS algorithm 208—209 see "Sliding
Transform domain LMS algorithm, comparison with the conventional LMS algorithm 218 219
Transform domain LMS algorithm, comparisons among different transforms 221—223
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