英文版PDF格式
Advanced Digital Signal Processing and Noise Reduction, Second Edition.
Saeed V. Vaseghi
Copyright © 2000 John Wiley & Sons Ltd
ISBNs: 0-471-62692-9 (Hardback): 0-470-84162-1 (Electronic)
CONTENTS
PREFACE ....................................................................................... xvii
FREQUENTLY USED SYMBOLS AND ABBREVIATIONS.......... xxi
CHAPTER 1 INTRODUCTION...............................................................1
1.1 Signals and Information...................................................................2
1.2 Signal Processing Methods..............................................................3
1.2.1 Non−parametric Signal Processing .....................................3
1.2.2 Model-Based Signal Processing ..........................................4
1.2.3 Bayesian Statistical Signal Processing ................................4
1.2.4 Neural Networks..................................................................5
1.3 Applications of Digital Signal Processing .......................................5
1.3.1 Adaptive Noise Cancellation and Noise Reduction ............5
1.3.2 Blind Channel Equalisation.................................................8
1.3.3 Signal Classification and Pattern Recognition ....................9
1.3.4 Linear Prediction Modelling of Speech.............................11
1.3.5 Digital Coding of Audio Signals .......................................12
1.3.6 Detection of Signals in Noise............................................14
1.3.7 Directional Reception of Waves: Beam-forming ..............16
1.3.8 Dolby Noise Reduction .....................................................18
1.3.9 Radar Signal Processing: Doppler Frequency Shift ..........19
1.4 Sampling and Analog–to–Digital Conversion ...............................21
1.4.1 Time-Domain Sampling and Reconstruction of Analog
Signals ..............................................................................22
1.4.2 Quantisation.......................................................................25
Bibliography.........................................................................................27
CHAPTER 2 NOISE AND DISTORTION...........................................29
2.1 Introduction....................................................................................30
2.2 White Noise ...................................................................................31
2.3 Coloured Noise ..............................................................................33
2.4 Impulsive Noise .............................................................................34
2.5 Transient Noise Pulses...................................................................35
2.6 Thermal Noise................................................................................36
viii Contents
2.7 Shot Noise......................................................................................38
2.8 Electromagnetic Noise ...................................................................38
2.9 Channel Distortions .......................................................................39
2.10 Modelling Noise ..........................................................................40
2.10.1 Additive White Gaussian Noise Model (AWGN)...........42
2.10.2 Hidden Markov Model for Noise ....................................42
Bibliography.........................................................................................43
CHAPTER 3 PROBABILITY MODELS ..............................................44
3.1 Random Signals and Stochastic Processes ....................................45
3.1.1 Stochastic Processes ..........................................................47
3.1.2 The Space or Ensemble of a Random Process ..................47
3.2 Probabilistic Models ......................................................................48
3.2.1 Probability Mass Function (pmf).......................................49
3.2.2 Probability Density Function (pdf)....................................50
3.3 Stationary and Non-Stationary Random Processes........................53
3.3.1 Strict-Sense Stationary Processes......................................55
3.3.2 Wide-Sense Stationary Processes......................................56
3.3.3 Non-Stationary Processes..................................................56
3.4 Expected Values of a Random Process..........................................57
3.4.1 The Mean Value ................................................................58
3.4.2 Autocorrelation..................................................................58
3.4.3 Autocovariance..................................................................59
3.4.4 Power Spectral Density .....................................................60
3.4.5 Joint Statistical Averages of Two Random Processes.......62
3.4.6 Cross-Correlation and Cross-Covariance ..........................62
3.4.7 Cross-Power Spectral Density and Coherence ..................64
3.4.8 Ergodic Processes and Time-Averaged Statistics .............64
3.4.9 Mean-Ergodic Processes ...................................................65
3.4.10 Correlation-Ergodic Processes ........................................66
3.5 Some Useful Classes of Random Processes ..................................68
3.5.1 Gaussian (Normal) Process ...............................................68
3.5.2 Multivariate Gaussian Process ..........................................69
3.5.3 Mixture Gaussian Process .................................................71
3.5.4 A Binary-State Gaussian Process ......................................72
3.5.5 Poisson Process .................................................................73
3.5.6 Shot Noise .........................................................................75
3.5.7 Poisson–Gaussian Model for Clutters and Impulsive
Noise.................................................................................77
3.5.8 Markov Processes..............................................................77
3.5.9 Markov Chain Processes ...................................................79
Contents ix
3.6 Transformation of a Random Process............................................81
3.6.1 Monotonic Transformation of Random Processes ............81
3.6.2 Many-to-One Mapping of Random Signals ......................84
3.7 Summary........................................................................................86
Bibliography.........................................................................................87
CHAPTER 4 BAYESIAN ESTIMATION.............................................89
4.1 Bayesian Estimation Theory: Basic Definitions ............................90
4.1.1 Dynamic and Probability Models in Estimation................91
4.1.2 Parameter Space and Signal Space....................................92
4.1.3 Parameter Estimation and Signal Restoration ...................93
4.1.4 Performance Measures and Desirable Properties of
Estimators.........................................................................94
4.1.5 Prior and Posterior Spaces and Distributions ....................96
4.2 Bayesian Estimation.....................................................................100
4.2.1 Maximum A Posteriori Estimation .................................101
4.2.2 Maximum-Likelihood Estimation ...................................102
4.2.3 Minimum Mean Square Error Estimation .......................105
4.2.4 Minimum Mean Absolute Value of Error Estimation.....107
4.2.5 Equivalence of the MAP, ML, MMSE and MAVE for
Gaussian Processes With Uniform Distributed
Parameters ......................................................................108
4.2.6 The Influence of the Prior on Estimation Bias and
Variance..........................................................................109
4.2.7 The Relative Importance of the Prior and the
Observation.....................................................................113
4.3 The Estimate–Maximise (EM) Method .......................................117
4.3.1 Convergence of the EM Algorithm .................................118
4.4 Cramer–Rao Bound on the Minimum Estimator Variance..........120
4.4.1 Cramer–Rao Bound for Random Parameters ..................122
4.4.2 Cramer–Rao Bound for a Vector Parameter....................123
4.5 Design of Mixture Gaussian Models ...........................................124
4.5.1 The EM Algorithm for Estimation of Mixture Gaussian
Densities .........................................................................125
4.6 Bayesian Classification ................................................................127
4.6.1 Binary Classification .......................................................129
4.6.2 Classification Error..........................................................131
4.6.3 Bayesian Classification of Discrete-Valued Parameters .132
4.6.4 Maximum A Posteriori Classification.............................133
4.6.5 Maximum-Likelihood (ML) Classification.....................133
4.6.6 Minimum Mean Square Error Classification ..................134
4.6.7 Bayesian Classification of Finite State Processes ...........134
x Contents
4.6.8 Bayesian Estimation of the Most Likely State
Sequence.........................................................................136
4.7 Modelling the Space of a Random Process..................................138
4.7.1 Vector Quantisation of a Random Process......................138
4.7.2 Design of a Vector Quantiser: K-Means Clustering........138
4.8 Summary......................................................................................140
Bibliography.......................................................................................141
CHAPTER 5 HIDDEN MARKOV MODELS.....................................143
5.1 Statistical Models for Non-Stationary Processes .........................144
5.2 Hidden Markov Models ...............................................................146
5.2.1 A Physical Interpretation of Hidden Markov Models .....148
5.2.2 Hidden Markov Model as a Bayesian Model ..................149
5.2.3 Parameters of a Hidden Markov Model ..........................150
5.2.4 State Observation Models ...............................................150
5.2.5 State Transition Probabilities ..........................................152
5.2.6 State–Time Trellis Diagram ............................................153
5.3 Training Hidden Markov Models ................................................154
5.3.1 Forward–Backward Probability Computation.................155
5.3.2 Baum–Welch Model Re-Estimation ...............................157
5.3.3 Training HMMs with Discrete Density Observation
Models ............................................................................159
5.3.4 HMMs with Continuous Density Observation Models ...160
5.3.5 HMMs with Mixture Gaussian pdfs................................161
5.4 Decoding of Signals Using Hidden Markov Models...................163
5.4.1 Viterbi Decoding Algorithm............................................165
5.5 HMM-Based Estimation of Signals in Noise...............................167
5.6 Signal and Noise Model Combination and Decomposition.........170
5.6.1 Hidden Markov Model Combination ..............................170
5.6.2 Decomposition of State Sequences of Signal and Noise.171
5.7 HMM-Based Wiener Filters ........................................................172
5.7.1 Modelling Noise Characteristics .....................................174
5.8 Summary......................................................................................174
Bibliography.......................................................................................175
CHAPTER 6 WIENER FILTERS........................................................178
6.1 Wiener Filters: Least Square Error Estimation ............................179
6.2 Block-Data Formulation of the Wiener Filter..............................184
6.2.1 QR Decomposition of the Least Square Error Equation .185
Contents xi
6.3 Interpretation of Wiener Filters as Projection in Vector Space ...187
6.4 Analysis of the Least Mean Square Error Signal .........................189
6.5 Formulation of Wiener Filters in the Frequency Domain............191
6.6 Some Applications of Wiener Filters...........................................192
6.6.1 Wiener Filter for Additive Noise Reduction ...................193
6.6.2 Wiener Filter and the Separability of Signal and Noise ..195
6.6.3 The Square-Root Wiener Filter .......................................196
6.6.4 Wiener Channel Equaliser...............................................197
6.6.5 Time-Alignment of Signals in Multichannel/Multisensor
Systems...........................................................................198
6.6.6 Implementation of Wiener Filters ...................................200
6.7 The Choice of Wiener Filter Order ..............................................201
6.8 Summary......................................................................................202
Bibliography.......................................................................................202
CHAPTER 7 ADAPTIVE FILTERS....................................................205
7.1 State-Space Kalman Filters..........................................................206
7.2 Sample-Adaptive Filters ..............................................................212
7.3 Recursive Least Square (RLS) Adaptive Filters ..........................213
7.4 The Steepest-Descent Method .....................................................219
7.5 The LMS Filter ............................................................................222
7.6 Summary......................................................................................224
Bibliography.......................................................................................225
CHAPTER 8 LINEAR PREDICTION MODELS..............................227
8.1 Linear Prediction Coding.............................................................228
8.1.1 Least Mean Square Error Predictor .................................231
8.1.2 The Inverse Filter: Spectral Whitening ...........................234
8.1.3 The Prediction Error Signal.............................................236
8.2 Forward, Backward and Lattice Predictors..................................236
8.2.1 Augmented Equations for Forward and Backward
Predictors........................................................................239
8.2.2 Levinson–Durbin Recursive Solution .............................239
8.2.3 Lattice Predictors.............................................................242
8.2.4 Alternative Formulations of Least Square Error
Prediction........................................................................244
8.2.5 Predictor Model Order Selection.....................................245
8.3 Short-Term and Long-Term Predictors........................................247
xii Contents
8.4 MAP Estimation of Predictor Coefficients..................................249
8.4.1 Probability Density Function of Predictor Output...........249
8.4.2 Using the Prior pdf of the Predictor Coefficients............251
8.5 Sub-Band Linear Prediction Model .............................................252
8.6 Signal Restoration Using Linear Prediction Models...................254
8.6.1 Frequency-Domain Signal Restoration Using Prediction
Models ............................................................................257
8.6.2 Implementation of Sub-Band Linear Prediction Wiener
Filters..............................................................................259
8.7 Summary......................................................................................261
Bibliography.......................................................................................261
CHAPTER 9 POWER SPECTRUM AND CORRELATION...........263
9.1 Power Spectrum and Correlation .................................................264
9.2 Fourier Series: Representation of Periodic Signals .....................265
9.3 Fourier Transform: Representation of Aperiodic Signals............267
9.3.1 Discrete Fourier Transform (DFT)..................................269
9.3.2 Time/Frequency Resolutions, The Uncertainty Principle
..................................................................................................269
9.3.3 Energy-Spectral Density and Power-Spectral Density ....270
9.4 Non-Parametric Power Spectrum Estimation ..............................272
9.4.1 The Mean and Variance of Periodograms .......................272
9.4.2 Averaging Periodograms (Bartlett Method) ....................273
9.4.3 Welch Method: Averaging Periodograms from
Overlapped and Windowed Segments............................274
9.4.4 Blackman–Tukey Method ...............................................276
9.4.5 Power Spectrum Estimation from Autocorrelation of
Overlapped Segments.....................................................277
9.5 Model-Based Power Spectrum Estimation ..................................278
9.5.1 Maximum–Entropy Spectral Estimation .........................279
9.5.2 Autoregressive Power Spectrum Estimation ...................282
9.5.3 Moving-Average Power Spectrum Estimation................283
9.5.4 Autoregressive Moving-Average Power Spectrum
Estimation.......................................................................284
9.6 High-Resolution Spectral Estimation Based on Subspace Eigen-
Analysis ......................................................................................284
9.6.1 Pisarenko Harmonic Decomposition...............................285
9.6.2 Multiple Signal Classification (MUSIC) Spectral
Estimation.......................................................................288
9.6.3 Estimation of Signal Parameters via Rotational
Invariance Techniques (ESPRIT)...................................292
Contents xiii
9.7 Summary......................................................................................294
Bibliography.......................................................................................294
CHAPTER 10 INTERPOLATION.......................................................297
10.1 Introduction................................................................................298
10.1.1 Interpolation of a Sampled Signal .................................298
10.1.2 Digital Interpolation by a Factor of I.............................300
10.1.3 Interpolation of a Sequence of Lost Samples ................301
10.1.4 The Factors That Affect Interpolation Accuracy...........303
10.2 Polynomial Interpolation............................................................304
10.2.1 Lagrange Polynomial Interpolation ...............................305
10.2.2 Newton Polynomial Interpolation .................................307
10.2.3 Hermite Polynomial Interpolation .................................309
10.2.4 Cubic Spline Interpolation.............................................310
10.3 Model-Based Interpolation ........................................................313
10.3.1 Maximum A Posteriori Interpolation ............................315
10.3.2 Least Square Error Autoregressive Interpolation ..........316
10.3.3 Interpolation Based on a Short-Term Prediction Model
..................................................................................................317
10.3.4 Interpolation Based on Long-Term and Short-term
Correlations..................................................................320
10.3.5 LSAR Interpolation Error..............................................323
10.3.6 Interpolation in Frequency–Time Domain ....................326
10.3.7 Interpolation Using Adaptive Code Books....................328
10.3.8 Interpolation Through Signal Substitution ....................329
10.4 Summary....................................................................................330
Bibliography.......................................................................................331
CHAPTER 11 SPECTRAL SUBTRACTION.....................................333
11.1 Spectral Subtraction...................................................................334
11.1.1 Power Spectrum Subtraction .........................................337
11.1.2 Magnitude Spectrum Subtraction..................................338
11.1.3 Spectral Subtraction Filter: Relation to Wiener Filters .339
11.2 Processing Distortions ...............................................................340
11.2.1 Effect of Spectral Subtraction on Signal Distribution...342
11.2.2 Reducing the Noise Variance ........................................343
11.2.3 Filtering Out the Processing Distortions .......................344
11.3 Non-Linear Spectral Subtraction ...............................................345
11.4 Implementation of Spectral Subtraction ....................................348
11.4.1 Application to Speech Restoration and Recognition.....351
xiv Contents
11.5 Summary....................................................................................352
Bibliography.......................................................................................352
CHAPTER 12 IMPULSIVE NOISE ....................................................355
12.1 Impulsive Noise .........................................................................356
12.1.1 Autocorrelation and Power Spectrum of Impulsive
Noise ............................................................................359
12.2 Statistical Models for Impulsive Noise......................................360
12.2.1 Bernoulli–Gaussian Model of Impulsive Noise ............360
12.2.2 Poisson–Gaussian Model of Impulsive Noise...............362
12.2.3 A Binary-State Model of Impulsive Noise ....................362
12.2.4 Signal to Impulsive Noise Ratio....................................364
12.3 Median Filters ............................................................................365
12.4 Impulsive Noise Removal Using Linear Prediction Models .....366
12.4.1 Impulsive Noise Detection ............................................367
12.4.2 Analysis of Improvement in Noise Detectability ..........369
12.4.3 Two-Sided Predictor for Impulsive Noise Detection ....372
12.4.4 Interpolation of Discarded Samples ..............................372
12.5 Robust Parameter Estimation.....................................................373
12.6 Restoration of Archived Gramophone Records.........................375
12.7 Summary....................................................................................376
Bibliography.......................................................................................377
CHAPTER 13 TRANSIENT NOISE PULSES....................................378
13.1 Transient Noise Waveforms ......................................................379
13.2 Transient Noise Pulse Models ..................................................381
13.2.1 Noise Pulse Templates .................................................382
13.2.2 Autoregressive Model of Transient Noise Pulses ........383
13.2.3 Hidden Markov Model of a Noise Pulse Process.........384
13.3 Detection of Noise Pulses ..........................................................385
13.3.1 Matched Filter for Noise Pulse Detection ....................386
13.3.2 Noise Detection Based on Inverse Filtering .................388
13.3.3 Noise Detection Based on HMM .................................388
13.4 Removal of Noise Pulse Distortions..........................................389
13.4.1 Adaptive Subtraction of Noise Pulses ...........................389
13.4.2 AR-based Restoration of Signals Distorted by Noise
Pulses ...........................................................................392
13.5 Summary....................................................................................395
Contents xv
Bibliography.......................................................................................395
CHAPTER 14 ECHO CANCELLATION...........................................396
14.1 Introduction: Acoustic and Hybrid Echoes ................................397
14.2 Telephone Line Hybrid Echo .....................................................398
14.3 Hybrid Echo Suppression ..........................................................400
14.4 Adaptive Echo Cancellation ......................................................401
14.4.1 Echo Canceller Adaptation Methods.............................403
14.4.2 Convergence of Line Echo Canceller............................404
14.4.3 Echo Cancellation for Digital Data Transmission.........405
14.5 Acoustic Echo ............................................................................406
14.6 Sub-Band Acoustic Echo Cancellation......................................411
14.7 Summary....................................................................................413
Bibliography.......................................................................................413
CHAPTER 15 CHANNEL EQUALIZATION AND BLIND
DECONVOLUTION....................................................416
15.1 Introduction................................................................................417
15.1.1 The Ideal Inverse Channel Filter ...................................418
15.1.2 Equalization Error, Convolutional Noise ......................419
15.1.3 Blind Equalization.........................................................420
15.1.4 Minimum- and Maximum-Phase Channels...................423
15.1.5 Wiener Equalizer...........................................................425
15.2 Blind Equalization Using Channel Input Power Spectrum........427
15.2.1 Homomorphic Equalization ..........................................428
15.2.2 Homomorphic Equalization Using a Bank of High-
Pass Filters ...................................................................430
15.3 Equalization Based on Linear Prediction Models......................431
15.3.1 Blind Equalization Through Model Factorisation.........433
15.4 Bayesian Blind Deconvolution and Equalization ......................435
15.4.1 Conditional Mean Channel Estimation .........................436
15.4.2 Maximum-Likelihood Channel Estimation...................436
15.4.3 Maximum A Posteriori Channel Estimation .................437
15.4.4 Channel Equalization Based on Hidden Markov
Models..........................................................................438
15.4.5 MAP Channel Estimate Based on HMMs.....................441
15.4.6 Implementations of HMM-Based Deconvolution .........442
15.5 Blind Equalization for Digital Communication Channels.........446
xvi Contents
15.5.1 LMS Blind Equalization................................................448
15.5.2 Equalization of a Binary Digital Channel......................451
15.6 Equalization Based on Higher-Order Statistics .........................453
15.6.1 Higher-Order Moments, Cumulants and Spectra ..........454
15.6.2 Higher-Order Spectra of Linear Time-Invariant
Systems ........................................................................457
15.6.3 Blind Equalization Based on Higher-Order Cepstra .....458
15.7 Summary....................................................................................464
Bibliography.......................................................................................465
INDEX.....................................................................................................467
站内商品搜索
