Advanced Digital Signal Processing and Noise Reduction
(3rd Edition 2006.2)
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【封面附图】:
【作 者】:Saeed V. Vaseghi
【ISBN 】:0-470-09494-X
【页数 】:480
【开本 】 :6.61x9.61英寸
【出版社】 :John Wiley & Sons Ltd
【出版日期】:2006.2
【文件格式】:
pdf(超清晰,8.60MB)
【目录】:
Abbreviations xxv
1 Introduction 1
1.1 Signals and Information 1
1.2 Signal Processing Methods 3
1.2.1 Transform-based Signal Processing 3
1.2.2 Model-based Signal Processing 4
1.2.3 Bayesian Signal Processing 4
1.2.4 Neural Networks 5
1.3 Applications of Digital Signal Processing 5
1.3.1 Adaptive Noise Cancellation 5
1.3.2 Adaptive Noise Reduction 6
1.3.3 Blind Channel Equalisation 7
1.3.4 Signal Classification and Pattern Recognition 8
1.3.5 Linear Prediction Modelling of Speech 9
1.3.6 Digital Coding of Audio Signals 10
1.3.7 Detection of Signals in Noise 12
1.3.8 Directional Reception of Waves: Beam-forming 13
1.3.9 Dolby Noise Reduction 15
1.3.10 Radar Signal Processing: Doppler Frequency Shift 15
1.4 Sampling and Analogue-to-digital Conversion 17
1.4.1 Sampling and Reconstruction of Analogue Signals 18
1.4.2 Quantisation 19
Bibliography 21
viii CONTENTS
2 Noise and Distortion 23
2.1 Introduction 24
2.2 White Noise 25
2.2.1 Band-limited White Noise 26
2.3 Coloured Noise 26
2.4 Impulsive Noise 27
2.5 Transient Noise Pulses 29
2.6 Thermal Noise 30
2.7 Shot Noise 31
2.8 Electromagnetic Noise 31
2.9 Channel Distortions 32
2.10 Echo and Multipath Reflections 33
2.11 Modelling Noise 33
2.11.1 Additive White Gaussian Noise Model 36
2.11.2 Hidden Markov Model for Noise 36
Bibliography 37
3 Probability and Information Models 39
3.1 Introduction 40
3.2 Random Signals 41
3.2.1 Random and Stochastic Processes 43
3.2.2 The Space of a Random Process 43
3.3 Probability Models 44
3.3.1 Probability and Random Variables 45
3.3.2 Probability Mass Function 45
3.3.3 Probability Density Function 47
3.3.4 Probability Density Functions of Random Processes 48
3.4 Information Models 50
3.4.1 Entropy 51
3.4.2 Mutual Information 54
3.4.3 Entropy Coding 56
3.5 Stationary and Nonstationary Random Processes 59
3.5.1 Strict-sense Stationary Processes 61
3.5.2 Wide-sense Stationary Processes 61
3.5.3 Nonstationary Processes 62
3.6 Statistics (Expected Values) of a Random Process 62
3.6.1 The Mean Value 63
3.6.2 Autocorrelation 63
3.6.3 Autocovariance 66
3.6.4 Power Spectral Density 66
3.6.5 Joint Statistical Averages of Two Random Processes 68
3.6.6 Cross-correlation and Cross-covariance 68
3.6.7 Cross-power Spectral Density and Coherence 70
3.6.8 Ergodic Processes and Time-averaged Statistics 70
3.6.9 Mean-ergodic Processes 70
3.6.10 Correlation-ergodic Processes 72
CONTENTS ix
3.7 Some Useful Classes of Random Processes 73
3.7.1 Gaussian (Normal) Process 73
3.7.2 Multivariate Gaussian Process 74
3.7.3 Mixture Gaussian Process 75
3.7.4 A Binary-state Gaussian Process 76
3.7.5 Poisson Process 77
3.7.6 Shot Noise 78
3.7.7 Poisson–Gaussian Model for Clutters and Impulsive Noise 79
3.7.8 Markov Processes 80
3.7.9 Markov Chain Processes 81
3.7.10 Gamma Probability Distribution 82
3.7.11 Rayleigh Probability Distribution 83
3.7.12 Laplacian Probability Distribution 83
3.8 Transformation of a Random Process 83
3.8.1 Monotonic Transformation of Random Processes 84
3.8.2 Many-to-one Mapping of Random Signals 86
3.9 Summary 90
Bibliography 90
4 Bayesian Inference 93
4.1 Bayesian Estimation Theory: Basic Definitions 94
4.1.1 Dynamic and Probability Models in Estimation 95
4.1.2 Parameter Space and Signal Space 96
4.1.3 Parameter Estimation and Signal Restoration 97
4.1.4 Performance Measures and Desirable Properties of Estimators 98
4.1.5 Prior and Posterior Spaces and Distributions 100
4.2 Bayesian Estimation 102
4.2.1 Maximum a Posteriori Estimation 103
4.2.2 Maximum-likelihood Estimation 104
4.2.3 Minimum Mean Square Error Estimation 107
4.2.4 Minimum Mean Absolute Value of Error Estimation 108
4.2.5 Equivalence of the MAP, ML, MMSE and MAVE for Gaussian
Processes with Uniform Distributed Parameters 109
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 114
4.3 The Estimate–Maximise Method 116
4.3.1 Convergence of the EM Algorithm 117
4.4 Cramer–Rao Bound on the Minimum Estimator Variance 119
4.4.1 Cramer–Rao Bound for Random Parameters 120
4.4.2 Cramer–Rao Bound for a Vector Parameter 121
4.5 Design of Gaussian Mixture Models 121
4.5.1 EM Estimation of Gaussian Mixture Model 122
4.6 Bayesian Classification 124
4.6.1 Binary Classification 125
4.6.2 Classification Error 127
4.6.3 Bayesian Classification of Discrete-valued Parameters 128
x CONTENTS
4.6.4 Maximum a Posteriori Classification 128
4.6.5 Maximum-likelihood Classification 129
4.6.6 Minimum Mean Square Error Classification 129
4.6.7 Bayesian Classification of Finite State Processes 130
4.6.8 Bayesian Estimation of the Most Likely State Sequence 131
4.7 Modelling the Space of a Random Process 132
4.7.1 Vector Quantisation of a Random Process 132
4.7.2 Vector Quantisation using Gaussian Models 133
4.7.3 Design of a Vector Quantiser: K-means Clustering 133
4.8 Summary 134
Bibliography 135
5 Hidden Markov Models 137
5.1 Statistical Models for Nonstationary Processes 138
5.2 Hidden Markov Models 139
5.2.1 Comparison of Markov and Hidden Markov Models 139
5.2.2 A Physical Interpretation: HMMs of Speech 141
5.2.3 Hidden Markov Model as a Bayesian Model 142
5.2.4 Parameters of a Hidden Markov Model 143
5.2.5 State Observation Probability Models 143
5.2.6 State Transition Probabilities 144
5.2.7 State–Time Trellis Diagram 145
5.3 Training Hidden Markov Models 145
5.3.1 Forward–Backward Probability Computation 147
5.3.2 Baum–Welch Model Re-estimation 148
5.3.3 Training HMMs with Discrete Density Observation Models 149
5.3.4 HMMs with Continuous Density Observation Models 150
5.3.5 HMMs with Gaussian Mixture pdfs 151
5.4 Decoding of Signals using Hidden Markov Models 152
5.4.1 Viterbi Decoding Algorithm 154
5.5 HMMs in DNA and Protein Sequence Modelling 155
5.6 HMMs for Modelling Speech and Noise 156
5.6.1 Modelling Speech with HMMs 156
5.6.2 HMM-based Estimation of Signals in Noise 156
5.6.3 Signal and Noise Model Combination and Decomposition 158
5.6.4 Hidden Markov Model Combination 159
5.6.5 Decomposition of State Sequences of Signal and Noise 160
5.6.6 HMM-based Wiener Filters 160
5.6.7 Modelling Noise Characteristics 162
5.7 Summary 162
Bibliography 163
6 Least Square Error Filters 165
6.1 Least Square Error Estimation: Wiener Filters 166
6.2 Block-data Formulation of the Wiener Filter 170
6.2.1 QR Decomposition of the Least Square Error Equation 171
CONTENTS xi
6.3 Interpretation of Wiener Filters as Projections in Vector Space 172
6.4 Analysis of the Least Mean Square Error Signal 174
6.5 Formulation of Wiener Filters in the Frequency Domain 175
6.6 Some Applications of Wiener Filters 177
6.6.1 Wiener Filters for Additive Noise Reduction 177
6.6.2 Wiener Filters and Separability of Signal and Noise 178
6.6.3 The Square-root Wiener Filter 179
6.6.4 Wiener Channel Equaliser 180
6.6.5 Time-alignment of Signals in Multichannel/Multisensor Systems 181
6.7 Implementation of Wiener Filters 182
6.7.1 The Choice of Wiener Filter Order 183
6.7.2 Improvements to Wiener Filters 184
6.8 Summary 185
Bibliography 185
7 Adaptive Filters 187
7.1 Introduction 188
7.2 State-space Kalman Filters 188
7.2.1 Derivation of the Kalman Filter Algorithm 190
7.3 Sample-adaptive Filters 195
7.4 Recursive Least Square Adaptive Filters 196
7.4.1 The Matrix Inversion Lemma 198
7.4.2 Recursive Time-update of Filter Coefficients 199
7.5 The Steepest-descent Method 201
7.5.1 Convergence Rate 203
7.5.2 Vector-valued Adaptation Step Size 204
7.6 The LMS Filter 204
7.6.1 Leaky LMS Algorithm 205
7.6.2 Normalised LMS Algorithm 206
7.7 Summary 207
Bibliography 208
8 Linear Prediction Models 209
8.1 Linear Prediction Coding 210
8.1.1 Frequency Response of LP Models 213
8.1.2 Calculation of Predictor Coefficients 214
8.1.3 Effect of Estimation of Correlation Function on LP Model Solution 216
8.1.4 The Inverse Filter: Spectral Whitening 216
8.1.5 The Prediction Error Signal 217
8.2 Forward, Backward and Lattice Predictors 219
8.2.1 Augmented Equations for Forward and Backward Predictors 220
8.2.2 Levinson–Durbin Recursive Solution 221
8.2.3 Lattice Predictors 223
8.2.4 Alternative Formulations of Least Square Error Prediction 224
8.2.5 Predictor Model Order Selection 225
8.3 Short- and Long-term Predictors 226
xii CONTENTS
8.4 MAP Estimation of Predictor Coefficients 228
8.4.1 Probability Density Function of Predictor Output 229
8.4.2 Using the Prior pdf of the Predictor Coefficients 230
8.5 Formant-tracking LP Models 230
8.6 Sub-band Linear Prediction Model 232
8.7 Signal Restoration using Linear Prediction Models 233
8.7.1 Frequency-domain Signal Restoration using Prediction Models 235
8.7.2 Implementation of Sub-band Linear Prediction Wiener Filters 237
8.8 Summary 238
Bibliography 238
9 Power Spectrum and Correlation 241
9.1 Power Spectrum and Correlation 242
9.2 Fourier Series: Representation of Periodic Signals 243
9.3 Fourier Transform: Representation of Aperiodic Signals 245
9.3.1 Discrete Fourier Transform 246
9.3.2 Time/Frequency Resolutions, the Uncertainty Principle 247
9.3.3 Energy-spectral Density and Power-spectral Density 248
9.4 Nonparametric Power Spectrum Estimation 249
9.4.1 The Mean and Variance of Periodograms 250
9.4.2 Averaging Periodograms (Bartlett Method) 250
9.4.3 Welch Method: Averaging Periodograms from Overlapped and
Windowed Segments 251
9.4.4 Blackman–Tukey Method 252
9.4.5 Power Spectrum Estimation from Autocorrelation of
Overlapped Segments 253
9.5 Model-based Power Spectrum Estimation 254
9.5.1 Maximum-entropy Spectral Estimation 255
9.5.2 Autoregressive Power Spectrum Estimation 257
9.5.3 Moving-average Power Spectrum Estimation 257
9.5.4 Autoregressive Moving-average Power Spectrum Estimation 258
9.6 High-resolution Spectral Estimation Based on Subspace Eigenanalysis 259
9.6.1 Pisarenko Harmonic Decomposition 259
9.6.2 Multiple Signal Classification Spectral Estimation 261
9.6.3 Estimation of Signal Parameters via Rotational Invariance
Techniques 264
9.7 Summary 265
Bibliography 266
10 Interpolation 267
10.1 Introduction 268
10.1.1 Interpolation of a Sampled Signal 268
10.1.2 Digital Interpolation by a Factor of I 269
10.1.3 Interpolation of a Sequence of Lost Samples 271
10.1.4 The Factors that affect Interpolation Accuracy 273
CONTENTS xiii
10.2 Polynomial Interpolation 274
10.2.1 Lagrange Polynomial Interpolation 275
10.2.2 Newton Polynomial Interpolation 276
10.2.3 Hermite Polynomial Interpolation 278
10.2.4 Cubic Spline Interpolation 278
10.3 Model-based Interpolation 280
10.3.1 Maximum a Posteriori Interpolation 281
10.3.2 Least Square Error Autoregressive Interpolation 282
10.3.3 Interpolation based on a Short-term Prediction Model 283
10.3.4 Interpolation based on Long- and Short-term Correlations 286
10.3.5 LSAR Interpolation Error 289
10.3.6 Interpolation in Frequency–Time Domain 290
10.3.7 Interpolation using Adaptive Codebooks 293
10.3.8 Interpolation through Signal Substitution 294
10.4 Summary 294
Bibliography 295
11 Spectral Amplitude Estimation 297
11.1 Introduction 298
11.1.1 Spectral Representation of Noisy Signals 299
11.1.2 Vector Representation of the Spectrum of Noisy Signals 299
11.2 Spectral Subtraction 300
11.2.1 Power Spectrum Subtraction 302
11.2.2 Magnitude Spectrum Subtraction 303
11.2.3 Spectral Subtraction Filter: Relation to Wiener Filters 303
11.2.4 Processing Distortions 304
11.2.5 Effect of Spectral Subtraction on Signal Distribution 305
11.2.6 Reducing the Noise Variance 306
11.2.7 Filtering Out the Processing Distortions 307
11.2.8 Nonlinear Spectral Subtraction 308
11.2.9 Implementation of Spectral Subtraction 310
11.3 Bayesian MMSE Spectral Amplitude Estimation 312
11.4 Application to Speech Restoration and Recognition 315
11.5 Summary 315
Bibliography 316
12 Impulsive Noise 319
12.1 Impulsive Noise 320
12.1.1 Autocorrelation and Power Spectrum of Impulsive Noise 322
12.2 Statistical Models for Impulsive Noise 323
12.2.1 Bernoulli–Gaussian Model of Impulsive Noise 324
12.2.2 Poisson–Gaussian Model of Impulsive Noise 324
12.2.3 A Binary-state Model of Impulsive Noise 325
12.2.4 Signal-to-impulsive-noise Ratio 326
xiv CONTENTS
12.3 Median Filters 327
12.4 Impulsive Noise Removal using Linear Prediction Models 328
12.4.1 Impulsive Noise Detection 328
12.4.2 Analysis of Improvement in Noise Detectability 330
12.4.3 Two-sided Predictor for Impulsive Noise Detection 331
12.4.4 Interpolation of Discarded Samples 332
12.5 Robust Parameter Estimation 333
12.6 Restoration of Archived Gramophone Records 334
12.7 Summary 335
Bibliography 336
13 Transient Noise Pulses 337
13.1 Transient Noise Waveforms 337
13.2 Transient Noise Pulse Models 339
13.2.1 Noise Pulse Templates 340
13.2.2 Autoregressive Model of Transient Noise Pulses 341
13.2.3 Hidden Markov Model of a Noise Pulse Process 342
13.3 Detection of Noise Pulses 342
13.3.1 Matched Filter for Noise Pulse Detection 343
13.3.2 Noise Detection based on Inverse Filtering 344
13.3.3 Noise Detection based on HMM 344
13.4 Removal of Noise Pulse Distortions 345
13.4.1 Adaptive Subtraction of Noise Pulses 345
13.4.2 AR-based Restoration of Signals Distorted
by Noise Pulses 347
13.5 Summary 349
Bibliography 349
14 Echo Cancellation 351
14.1 Introduction: Acoustic and Hybrid Echoes 352
14.2 Telephone Line Hybrid Echo 353
14.2.1 Echo: the Sources of Delay in Telephone Networks 354
14.2.2 Echo Return Loss 355
14.3 Hybrid Echo Suppression 355
14.4 Adaptive Echo Cancellation 356
14.4.1 Echo Canceller Adaptation Methods 357
14.4.2 Convergence of Line Echo Canceller 358
14.4.3 Echo Cancellation for Digital Data Transmission 359
14.5 Acoustic Echo 360
14.6 Sub-band Acoustic Echo Cancellation 363
14.7 Multiple-input Multiple-output Echo Cancellation 365
14.7.1 Stereophonic Echo Cancellation Systems 365
14.8 Summary 368
Bibliography 368
CONTENTS xv
15 Channel Equalisation and Blind Deconvolution 371
15.1 Introduction 372
15.1.1 The Ideal Inverse Channel Filter 373
15.1.2 Equalisation Error, Convolutional Noise 374
15.1.3 Blind Equalisation 374
15.1.4 Minimum- and Maximum-phase Channels 376
15.1.5 Wiener Equaliser 377
15.2 Blind Equalisation using the Channel Input Power Spectrum 379
15.2.1 Homomorphic Equalisation 380
15.2.2 Homomorphic Equalisation using a Bank of High-pass Filters 382
15.3 Equalisation based on Linear Prediction Models 382
15.3.1 Blind Equalisation through Model Factorisation 384
15.4 Bayesian Blind Deconvolution and Equalisation 385
15.4.1 Conditional Mean Channel Estimation 386
15.4.2 Maximum-likelihood Channel Estimation 386
15.4.3 Maximum a Posteriori Channel Estimation 386
15.4.4 Channel Equalisation based on Hidden Markov Models 387
15.4.5 MAP Channel Estimate based on HMMs 389
15.4.6 Implementations of HMM-based Deconvolution 390
15.5 Blind Equalisation for Digital Communications Channels 393
15.5.1 LMS Blind Equalisation 395
15.5.2 Equalisation of a Binary Digital Channel 397
15.6 Equalisation based on Higher-order Statistics 398
15.6.1 Higher-order Moments, Cumulants and Spectra 399
15.6.2 Higher-order Spectra of Linear Time-invariant Systems 401
15.6.3 Blind Equalisation based on Higher-order Cepstra 402
15.7 Summary 406
Bibliography 406
16 Speech Enhancement in Noise 409
16.1 Introduction 410
16.2 Single-input Speech-enhancement Methods 411
16.2.1 An Overview of a Speech-enhancement System 411
16.2.2 Wiener Filter for De-noising Speech 414
16.2.3 Spectral Subtraction of Noise 417
16.2.4 Bayesian MMSE Speech Enhancement 418
16.2.5 Kalman Filter 419
16.2.6 Speech Enhancement via LP Model Reconstruction 422
16.3 Multiple-input Speech-enhancement Methods 425
16.3.1 Beam-forming with Microphone Arrays 427
16.4 Speech Distortion Measurements 430
Bibliography 431
17 Noise in Wireless Communications 433
17.1 Introduction to Cellular Communications 434
17.2 Noise, Capacity and Spectral Efficiency 436
xvi CONTENTS
17.3 Communications Signal Processing in Mobile Systems 438
17.4 Noise and Distortion in Mobile Communications Systems 439
17.4.1 Multipath Propagation of Electromagnetic Signals 440
17.4.2 Rake Receivers for Multipath Signals 441
17.4.3 Signal Fading in Mobile Communications Systems 442
17.4.4 Large-scale Signal Fading 443
17.4.5 Small-scale Fast Signal Fading 444
17.5 Smart Antennas 444
17.5.1 Switched and Adaptive Smart Antennas 446
17.5.2 Space–Time Signal Processing – Diversity Schemes 446
17.6 Summary 447
Bibliography 448
Index
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