Front Matter and Index (779802), страница 3
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an HMMAdaptation convergence factorExpected mean of vector xNoiseA noise vector of N samplesImpulsive noiseNoise spectrumComplex conjugate of N(f)Time-averaged noise spectrumA Gaussian pdf with mean vector µ xx andcovariance matrix Σ xxIn the order of (· )Filter order (length)Probability density functionProbability mass functionProbability mass function of xiJoint probability mass function of xi and y jConditional probability mass function of xi givenyjPower spectrum of noise n(m)Power spectrum of the signal x(m)Frequently Used Symbols and AbbreviationsPXY ( f )θθˆrkr xx (m)rxx (m)RxxRxyss MLSNRSINRσ n2Σ nnΣ xxσ 2xσ n2x(m)xˆ (m)x(m)X(f)X*(f)X(f )X(f,t)XXHy(m)y(m)yˆ (m m − i)YYHVarwkw(m)W(f)zxxiiiCross−power spectrum of signals x(m) and y(m)Parameter vectorEstimate of the parameter vector θReflection coefficientsAutocorrelation functionAutocorrelation vectorAutocorrelation matrix of signal x(m)Cross−correlation matrixState sequenceMaximum−likelihood state sequenceSignal-to-noise ratioSignal-to-impulsive noise ratioVariance of noise n(m)Covariance matrix of noise n(m)Covariance matrix of signal x(m)Variance of signal x(m)Variance of noise n(m)Clean signalEstimate of clean signalClean signal vectorFrequency spectrum of signal x(m)Complex conjugate of X(f)Time-averaged frequency spectrum of x(m)Time-frequency spectrum of x(m)Clean signal matrixHermitian transpose of XNoisy signalNoisy signal vectorPrediction of y(m) based on observations up totime m–iNoisy signal matrixHermitian transpose of YVarianceWiener filter coefficientsWiener filter coefficients vectorWiener filter frequency responsez-transform variableAdvanced Digital Signal Processing and Noise Reduction, Second Edition.Saeed V.
VaseghiCopyright © 2000 John Wiley & Sons LtdISBNs: 0-471-62692-9 (Hardback): 0-470-84162-1 (Electronic)INDEXAAbsolute value of error, 374Acoustic feedbacks, 407Acoustic noise, 30Adaptation formula, 212Adaptation step size, 220, 404Adaptive filter, 205, 212, 448Adaptive noise cancellation, 6Additive white Gaussian noise, 42Algorithm, 165Aliasing, 23All-pole digital filter, 231Analog signals, 22Autocorrelation, 58, 271, 359Autocorrelation of impulsivenoise, 62Autocorrelation of the output of alinear time-invariant system,59Autocorrelation of white noise, 61Autocovariance, 59Autoregressive, 115, 278Autoregressive (AR) model, 46,78, 144, 316, 383Auto regressive-moving-averagemodel, 278AWGN, 109BBackward predictor, 237Backward probability, 156Band-limited white noise, 31, 32Bartlett periodogram, 273Baum–Welch model reEstimation, 157Bayes' rule, 50, 167, 249Bayesian estimation, 89, 100Bayesian inference, 4Bayesian MMSE, 105Bayesian risk function, 100Beam-forming, 16Bernoulli-Gaussian model, 360Bias, 94Bi-cepstrum, 459Binary-state classifier, 9Binary-state Gaussian Process, 72Bi-spectrum, 457Bivariate pdf, 51Block least square (BLS) errorestimation, 185Boltzmann constant, 37Brown noise, 33Brownian motion, 47Burg's method, 244CCar noise, 41Central limit theorem, 65, 68, 449Channel distortions, 30, 39, 416Channel equalisation, 8,416Channel impulse response, 34,358Channel response, 417Characteristic function, 454Classification, 127Clutters, 77Coherence, 64Coloured Noise, 33468Complete data, 117Conditional multivariate Gaussianprobability, 70Conditional probability density,52Consistent estimator, 95Continuous density HMM, 151,160Continuously variable stateprocess, 144Continuous-valued randomvariables, 51Convergence rate, 222Convolutional noise, 449Correlation subtraction, 255Correlation-ergodic, 67, 183Correlator, 14Cost function, 374Cost of error function, 100, 374Cramer-Rao lower bound, 120Cross-correlation, 62, 390Cross-covariance, 63Cross-power spectral density, 64Cumulants, 455Cumulative distribution function,51DDecision-directed equalisation,444Decoding of signals, 163Deconvolution, 417Decorrelation filter, 235Detection, 367Detection of signals in noise, 14Deterministic signals, 45DFT, 349Digital coding of audio, 12Digital signal, 21IndexDiscrete Density ObservationModels, 159Discrete Fourier transform, 13,269Discrete state observation HMM,151Discrete-time stochastic process,47Discrete-valued random variable,50Distortion, 29Distortion matrix, 206Distribution function, 69Divided differences, 308Dolby, 18Doppler, 20Durbins algorithm, 242EEcho Cancellation, 396Echo canceller, 401Echo suppresser, 400Echo synthesiser, 411Efficient estimator, 95Eigenvalue, 221Eigenvalue spread, 222Eigen analysis, 284Electromagnetic noise, 30, 38Electrostatic noise, 30EM Algorithm, 118Energy-spectral density, 270Ensemble, 47Entropy, 279Equalisation, 417Ergodic HMM, 147Ergodic processes, 47,64ESPIRIT algorithm, 292Estimate–Maximise (EM), 117Estimation, 90469IndexEstimation of the Mean andVariance of a GaussianProcess, 102Expected values, 57Huber's function, 374Hybrid echo, 398Hypothesised-input HMMequalisation, 443FIFactorisation of linear predictionmodels, 433Finite state process, 144Fisher's information matrix, 123Forgetting factor, 215Forward predictor model, 236Forward probability, 155Fourier series, 265Fourier transform, 267Frequency resolution, 270Ideal equaliser, 418Ideal interpolation, 298Impulsive noise, 31, 34, 355Incomplete data, 117Influence function, 374Information, 2Inhomogeneous Markov chains,80Innovation signal, 206, 230, 255Inversion lemma, 216Interpolation, 297Interpolation error, 323Interpolation through signalsubstitution, 329Inter-symbol-interference, 446Inverse discrete Fourier transform,269Inverse filter, 234Inverse linear predictor, 234Inverse-channel filter, 418GGaussian pdf, 151Gaussian process, 68Gaussian-AR process, 115Gauss–Markov process, 79HHard non-linearity, 452Hermite polynomials, 309Hermitian transpose, 289Hidden Markov model, 73, 143,363, 438Hidden Markov model for Noise,42High resolution spectralestimation, 284Higher-Order Spectra, 456Homogeneous Poisson process,74Homogenous Markov chain, 80Homomorphic equalisation, 428Howling, 407JJacobian, 85Joint characteristic function, 454KKalman filter, 206Kalman filtering algorithm, 210Kalman gain, 208K-means algorithm, 138Kronecker delta function, 359470LLagrange interpolation, 305Leaky LMS algorithm, 224Least squared AR (LSAR)interpolation, 320Left–right HMM, 148Levinson–Durbin algorithm, 238,239Linear array, 16Linear least square error filters,178Linear prediction, 228Linear prediction models, 11, 227,431Linear time invariant channel, 197Linear transformation, 86Linear transformation of aGaussian process, 86Line interpolator, 306LMS adaptation algorithm, 405LMS Filter, 222Log-normal Process, 83MMagnitude spectral subtraction,335Many-to-one Mapping, 84MAP Estimation, 114Marginal density, 78Marginal probabilities, 73Marginal probability massfunctions, 50Markov chain, 79Markov process, 77Markovian prior, 439Markovian state transition prior,149M-ary pulse amplitudemodulation, 446, 450Matched filter, 14, 386IndexMatrix inversion lemma, 216Maximum a posteriori (MAP)estimate, 101, 251Maximum entropy correlation,280Maximum-phase channel, 423,458Maximum-phase information, 461Mean value of a process, 58Mean-ergodic, 65Median, 107Median Filters, 365Minimisation of Backward andForward Prediction Error,245Minimum mean absolute value oferror, 107Minimum mean squared error,181Minimum-phase channel, 423Minimum-phase information, 461Mixture Gaussian densities, 72Mixture Gaussian density, 151Mixture pdf, 450Model order selection, 245Model-based signal processing, 4Modelling noise, 40, 174Monotonic transformation, 81Moving-average, 278Multivariate Gaussian pdf, 69Multi-variate probability massfunctions, 52MUSIC algorithm, 288Musical noise, 341, 344M-variate pdf, 52NNarrowband noise, 31Neural networks, 5Newton polynomials, 307471IndexNoise, 29Noise reduction, 193Non-linear spectral subtraction,345Nonstationary process, 53, 56,144Normal process, 68Normalised least mean squareerror, 404Nyquist sampling theorem, 23,298OObservation equation, 206Orthogonality, 265Outlier, 365Over-subtraction, 345PParameter estimation, 93Parameter Space, 92Parseval's theorem, 191Partial correlation, 241Partial correlation (PARCOR)coefficients, 244Pattern recognition, 9Performance Measures, 94Periodogram, 272Pink noise, 33Poisson process, 73Poisson–Gaussian model, 362Poles and zeros, 433Posterior pdf, 90, 97Power, 55Power spectral density, 60, 271Power spectral subtraction, 335Power spectrum, 192, 264, 272,359, 428Power Spectrum Estimation, 263Power spectrum of a white noise,61Power Spectrum of impulsiveNoise., 61Power spectrum subtraction, 337Prediction error filter, 235Prediction error signal, 236Predictive model, 91Principal eigenvectors., 290Prior pdf, 97Prior pdf of predictor coefficients,251Prior space of a signal, 96Probability density function, 51Probability mass function, 50Probability models, 48Processing distortions, 341, 344Processing noise, 30QQR Decomposition, 185Quantisation, 22Quantisation noise, 25RRadar, 19Random signals, 45Random variable, 48Rayner, 433Rearrangement matrices, 314Recursive least square error (RLS)filter, 213Reflection coefficient, 240, 242RLS adaptation algorithm, 218Robust estimator, 373Rotation matrix, 292SSample and hold, 22, 24Sampling, 22, 23472Scalar Gaussian random variable,68Second order statistics, 60Short time Fourier transform(STFT), 326Shot noise, 38, 76Signal, 2Signal classification, 9Signal restoration, 93Signal to impulsive noise ratio,364Signal to noise ratio, 195Signal to quantisation noise ratio,25Signum non-linearity, 449SINR, 364Sinusoidal signal, 45Soft non-linearity, 453Source–filter model, 228Spectral coherence, 64Spectral subtraction, 335Spectral whitening, 234, 235Spectral–time representation, 326Speech processing, 11Speech recognition, 10State observation models, 150State transition probability, 158State transition-probability matrix,150State-dependent Wiener filters,173State-equation model, 206State–time diagram, 153Statistical models, 44, 91Stochastic processes, 47Strict-sense stationary process, 55Subspace eigen-analysis, 284TThermal noise, 36IndexTime-delay estimation, 63Time delay of arrival, 198Time/Frequency Resolutions, 269Time-Alignment, 198Time-averaged correlations, 183Time-varying processes, 56Toeplitz matrix, 183, 233Transformation of a randomprocess, 81Transform-based coder, 13Transient noise pulses, 31, 379Transient Noise Pulses, 35Trellis, 153Tri-cepstrum, 461Tri-spectrum, 457Tukeys bi-weight function, 374UUnbiased estimator, 94Uncertainty principle, 269Uniform cost function, 101Uni-variate pdf, 51VVandermonde matrix, 305Vector quantisation, 138Vector space, 188Viterbi decoding, 143WWelch power spectrum, 275White noise, 61White Noise, 31Wide-sense stationary processes,56Wiener equalisation, 425Wiener filter, 7, 172, 178, 179,339473IndexWiener filter in frequencydomain, 191Wiener-Kinchin, 60ZZero-forcing filter, 447Zero-inserted signal, 300.
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