Advanced Digital Signal Processing and Noise Reduction

Advanced Digital Signal Processing and Noise Reduction......Page 1
CONTENTS......Page 5
PREFACE......Page 15
FREQUENTLY USED SYMBOLS AND ABBR......Page 18
1 - INTRODUCTION......Page 21
1.1 Signals and Information......Page 22
1.2 Signal Processing Methods......Page 23
1.3 Applications of Digital Signal Processing......Page 25
1.4 Sampling and Analog–to–Digital Conversion......Page 41
Bibliography......Page 47
2 - NOISE AND DISTORTION......Page 49
2.1 Introduction......Page 50
2.2 White Noise......Page 51
2.3 Coloured Noise......Page 53
2.4 Impulsive Noise......Page 54
2.5 Transient Noise Pulses......Page 55
2.6 Thermal Noise......Page 57
2.8 Electromagnetic Noise......Page 58
2.9 Channel Distortions......Page 59
2.10 Modelling Noise......Page 60
Bibliography......Page 63
3 - PROBABILITY MODELS......Page 64
3.1 Random Signals and Stochastic Processes......Page 65
3.2 Probabilistic Models......Page 68
3.3 Stationary and Non-Stationary Random Processes......Page 73
3.4 Expected Values of a Random Process......Page 77
3.5 Some Useful Classes of Random Processes......Page 88
3.6 Transformation of a Random Process......Page 101
3.7 Summary......Page 106
Bibliography......Page 107
4 - BAYESIAN ESTIMATION......Page 109
4.1 Bayesian Estimation Theory: Basic Definitions......Page 110
4.2 Bayesian Estimation......Page 120
4.3 The Estimate–Maximise (EM) Method......Page 137
4.4 Cramer–Rao Bound on the Minimum Estimator Variance......Page 140
4.5 Design of Mixture Gaussian Models......Page 144
4.6 Bayesian Classification......Page 147
4.7 Modelling the Space of a Random Process......Page 158
4.8 Summary......Page 160
Bibliography......Page 161
5 - HIDDEN MARKOV MODELS......Page 163
5.1 Statistical Models for Non-Stationary Processes......Page 164
5.2 Hidden Markov Models......Page 166
5.3 Training Hidden Markov Models......Page 174
5.4 Decoding of Signals Using Hidden Markov Models......Page 183
5.5 HMM-Based Estimation of Signals in Noise......Page 187
5.6 Signal and Noise Model Combination and Decomposition......Page 190
5.7 HMM-Based Wiener Filters......Page 192
5.8 Summary......Page 194
Bibliography......Page 195
6 - WIENER FILTERS......Page 198
6.1 Wiener Filters: Least Square Error Estimation......Page 199
6.2 Block-Data Formulation of the Wiener Filter......Page 204
6.3 Interpretation of Wiener Filters as Projection in Vector Space......Page 207
6.4 Analysis of the Least Mean Square Error Signal......Page 209
6.5 Formulation of Wiener Filters in the Frequency Domain......Page 211
6.6 Some Applications of Wiener Filters......Page 212
6.7 The Choice of Wiener Filter Order......Page 221
Bibliography......Page 222
7 - ADAPTIVE FILTERS......Page 225
7.1 State-Space Kalman Filters......Page 226
7.2 Sample-Adaptive Filters......Page 232
7.3 Recursive Least Square (RLS) Adaptive Filters......Page 233
7.4 The Steepest-Descent Method......Page 239
7.5 The LMS Filter......Page 242
7.6 Summary......Page 244
Bibliography......Page 245
8 - LINEAR PREDICTION MODELS......Page 247
8.1 Linear Prediction Coding......Page 248
8.2 Forward, Backward and Lattice Predictors......Page 256
8.3 Short-Term and Long-Term Predictors......Page 267
8.4 MAP Estimation of Predictor Coefficients......Page 269
8.5 Sub-Band Linear Prediction Model......Page 272
8.6 Signal Restoration Using Linear Prediction Models......Page 274
Bibliography......Page 281
9 - POWER SPECTRUM AND CORRELATION......Page 283
9.1 Power Spectrum and Correlation......Page 284
9.2 Fourier Series: Representation of Periodic Signals......Page 285
9.3 Fourier Transform: Representation of Aperiodic Signals......Page 287
9.4 Non-Parametric Power Spectrum Estimation......Page 292
9.5 Model-Based Power Spectrum Estimation......Page 298
9.6 High-Resolution Spectral Estimation Based on Subspace Eigen-Analysis......Page 304
Bibliography......Page 314
10 - INTERPOLATION......Page 317
10.1 Introduction......Page 318
10.2 Polynomial Interpolation......Page 324
10.3 Model-Based Interpolation......Page 333
10.4 Summary......Page 350
Bibliography......Page 351
11 - SPECTRAL SUBTRACTION......Page 353
11.1 Spectral Subtraction......Page 354
11.2 Processing Distortions......Page 360
11.3 Non-Linear Spectral Subtraction......Page 365
11.4 Implementation of Spectral Subtraction......Page 368
Bibliography......Page 372
12 - IMPULSIVE NOISE......Page 375
12.1 Impulsive Noise......Page 376
12.2 Statistical Models for Impulsive Noise......Page 380
12.3 Median Filters......Page 385
12.4 Impulsive Noise Removal Using Linear Prediction Models......Page 386
12.5 Robust Parameter Estimation......Page 393
12.6 Restoration of Archived Gramophone Records......Page 395
12.7 Summary......Page 396
Bibliography......Page 397
13 - TRANSIENT NOISE PULSES......Page 398
13.1 Transient Noise Waveforms......Page 399
13.2 Transient Noise Pulse Models......Page 401
13.3 Detection of Noise Pulses......Page 405
13.4 Removal of Noise Pulse Distortions......Page 409
Bibliography......Page 415
14 - ECHO CANCELLATION......Page 416
14.1 Introduction: Acoustic and Hybrid Echoes......Page 417
14.2 Telephone Line Hybrid Echo......Page 418
14.3 Hybrid Echo Suppression......Page 420
14.4 Adaptive Echo Cancellation......Page 421
14.5 Acoustic Echo......Page 426
14.6 Sub-Band Acoustic Echo Cancellation......Page 431
Bibliography......Page 433
15 - CHANNEL EQUALIZATION AND BLIND DECONVOLUTION......Page 436
15.1 Introduction......Page 437
15.2 Blind Equalization Using Channel Input Power Spectrum......Page 447
15.3 Equalization Based on Linear Prediction Models......Page 451
15.4 Bayesian Blind Deconvolution and Equalization......Page 455
15.5 Blind Equalization for Digital Communication Channels......Page 466
15.6 Equalization Based on Higher-Order Statistics......Page 473
15.7 Summary......Page 484
Bibliography......Page 485
INDEX......Page 487