Advanced Digital Signal Processing and Noise Reduction / Edition 3

Advanced Digital Signal Processing and Noise Reduction / Edition 3

by Saeed V. Vaseghi
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Advanced Digital Signal Processing and Noise Reduction / Edition 3

Signal processing plays an increasingly central role in the development of modern telecommunication and information processing systems, with a wide range of applications in areas such as multimedia technology, audio-visual signal processing, cellular mobile communication, radar systems and financial data forecasting. The theory and application of signal processing deals with the identification, modelling and utilisation of patterns and structures in a signal process. The observation signals are often distorted, incomplete and noisy and hence, noise reduction and the removal of channel distortion is an important part of a signal processing system.

Advanced Digital Signal Processing and Noise Reduction, Third Edition, provides a fully updated and structured presentation of the theory and applications of statistical signal processing and noise reduction methods. Noise is the eternal bane of communications engineers, who are always striving to find new ways to improve the signal-to-noise ratio in communications systems and this resource will help them with this task.

Features two new chapters on Noise and Distortion and Noise in Wireless Communications. Topics discussed include: probability theory, Bayesian estimation and classification, hidden Markov models, adaptive filters, multi-band linear prediction, spectral estimation, and impulsive and transient noise removal. Explores practical solutions to interpolation of missing signals, echo cancellation, impulsive and transient noise removal, channel equalisation, HMM-based signal and noise decomposition. This is an invaluable text for senior undergraduates, postgraduates and researchers in the fields of digital signal processing,telecommunications and statistical data analysis. It will also appeal to engineers in telecommunications and audio and signal processing industries.

Product Details

ISBN-13: 9780470094945
Publisher: Wiley
Publication date: 01/06/2006
Edition description: Revised Edition
Pages: 480
Product dimensions: 6.91(w) x 10.06(h) x 1.31(d)

Table of Contents

Preface     xvii
Symbols     xxi
Abbreviations     xxv
Introduction     1
Signals and Information     1
Signal Processing Methods     3
Transform-based Signal Processing     3
Model-based Signal Processing     4
Bayesian Signal Processing     4
Neural Networks     5
Applications of Digital Signal Processing     5
Adaptive Noise Cancellation     5
Adaptive Noise Reduction     6
Blind Channel Equalisation     7
Signal Classification and Pattern Recognition     8
Linear Prediction Modelling of Speech     9
Digital Coding of Audio Signals     10
Detection of Signals in Noise     12
Directional Reception of Waves: Beam-forming     13
Dolby Noise Reduction     15
Radar Signal Processing: Doppler Frequency Shift     15
Sampling and Analogue-to-digital Conversion     17
Sampling and Reconstruction of Analogue Signals     18
Quantisation     19
Bibliography     21
Noise and Distortion     23
Introduction     24
White Noise     25
Band-limited White Noise     26
Coloured Noise     26
Impulsive Noise     27
Transient Noise Pulses     29
Thermal Noise     30
Shot Noise     31
Electromagnetic Noise     31
Channel Distortions     32
Echo and Multipath Reflections     33
Modelling Noise     33
Additive White Gaussian Noise Model     36
Hidden Markov Model for Noise     36
Bibliography     37
Probability and Information Models     39
Introduction     40
Random Signals     41
Random and Stochastic Processes     43
The Space of a Random Process     43
Probability Models     44
Probability and Random Variables     45
Probability Mass Function     45
Probability Density Function     47
Probability Dgnsity Functions of Random Processes     48
Information Models     50
Entropy     51
Mutual Information     54
Entropy Coding     56
Stationary and Nonstationary Random Processes     59
Strict-sense Stationary Processes     61
Wide-sense Stationary Processes     61
Nonstationary Processes     62
Statistics (Expected Values) of a Random Process     62
The Mean Value     63
Autocorrelation     63
Autocovariance     66
Power Spectral Density     66
Joint Statistical Averages of Two Random Processes     68
Cross-correlation and Cross-covariance     68
Cross-power Spectral Density and Coherence     70
Ergodic Processes and Time-averaged Statistics     70
Mean-ergodic Processes     70
Correlation-ergodic Processes     72
Some Useful Classes of Random Processes     73
Gaussian (Normal) Process     73
Multivariate Gaussian Process     74
Mixture Gaussian Process     75
A Binary-state Gaussian Process     76
Poisson Process     77
Shot Noise     78
Poisson-Gaussian Model for Clutters and Impulsive Noise     79
Markov Processes     80
Markov Chain Processes     81
Gamma Probability Distribution     82
Rayleigh Probability Distribution     83
Laplacian Probability Distribution     83
Transformation of a Random Process      83
Monotonic Transformation of Random Processes     84
Many-to-one Mapping of Random Signals     86
Summary     90
Bibliography     90
Bayesian Inference     93
Bayesian Estimation Theory: Basic Definitions     94
Dynamic and Probability Models in Estimation     95
Parameter Space and Signal Space     96
Parameter Estimation and Signal Restoration     97
Performance Measures and Desirable Properties of Estimators     98
Prior and Posterior Spaces and Distributions     100
Bayesian Estimation     102
Maximum a Posteriori Estimation     103
Maximum-likelihood Estimation     104
Minimum Mean Square Error Estimation     107
Minimum Mean Absolute Value of Error Estimation     108
Equivalence of the MAP, ML, MMSE and MAVE for Gaussian Processes with Uniform Distributed Parameters     109
The Influence of the Prior on Estimation Bias and Variance     109
The Relative Importance of the Prior and the Observation     114
The Estimate-Maximise Method     116
Convergence of the EM Algorithm     117
Cramer-Rao Bound on the Minimum Estimator Variance     119
Cramer-Rao Bound for Random Parameters     120
Cramer-Rao Bound for a Vector Parameter     121
Design of Gaussian Mixture Models     121
EM Estimation of Gaussian Mixture Model     122
Bayesian Classification     124
Binary Classification     125
Classification Error     127
Bayesian Classification of Discrete-valued Parameters     128
Maximum a Posteriori Classification     128
Maximum-likelihood Classification     129
Minimum Mean Square Error Classification     129
Bayesian Classification of Finite State Processes     130
Bayesian Estimation of the Most Likely State Sequence     131
Modelling the Space of a Random Process     132
Vector Quantisation of a Random Process     132
Vector Quantisation using Gaussian Models     133
Design of a Vector Quantiser: K-means Clustering     133
Summary     134
Bibliography     135
Hidden Markov Models     137
Statistical Models for Nonstationary Processes     138
Hidden Markov Models     139
Comparison of Markov and Hidden Markov Models     139
A Physical Interpretation: HMMs of Speech     141
Hidden Markov Model as a Bayesian Model     142
Parameters of a Hidden Markov Model     143
State Observation Probability Models     143
State Transition Probabilities     144
State-Time Trellis Diagram     145
Training Hidden Markov Models     145
Forward-Backward Probability Computation     147
Baum-Welch Model Re-estimation     148
Training HMMs with Discrete Density Observation Models     149
HMMs with Continuous Density Observation Models     150
HMMs with Gaussian Mixture pdfs     151
Decoding of Signals using Hidden Markov Models     152
Viterbi Decoding Algorithm     154
HMMs in DNA and Protein Sequence Modelling     155
HMMs for Modelling Speech and Noise     156
Modelling Speech with HMMs     156
HMM-based Estimation of Signals in Noise     156
Signal and Noise Model Combination and Decomposition     158
Hidden Markov Model Combination     159
Decomposition of State Sequences of Signal and Noise     160
HMM-based Wiener Filters     160
Modelling Noise Characteristics     162
Summary     162
Bibliography     163
Least Square Error Filters      165
Least Square Error Estimation: Wiener Filters     166
Block-data Formulation of the Wiener Filter     170
QR Decomposition of the Least Square Error Equation     171
Interpretation of Wiener Filters as Projections in Vector Space     172
Analysis of the Least Mean Square Error Signal     174
Formulation of Wiener Filters in the Frequency Domain     175
Some Applications of Wiener Filters     177
Wiener Filters for Additive Noise Reduction     177
Wiener Filters and Separability of Signal and Noise     178
The Square-root Wiener Filter     179
Wiener Channel Equaliser     180
Time-alignment of Signals in Multichannel/Multisensor Systems     181
Implementation of Wiener Filters     182
The Choice of Wiener Filter Order     183
Improvements to Wiener Filters     184
Summary     185
Bibliography     185
Adaptive Filters     187
Introduction     188
State-space Kalman Filters     188
Derivation of the Kalman Filter Algorithm     190
Sample-adaptive Filters     195
Recursive Least Square Adaptive Filters     196
The Matrix Inversion Lemma      198
Recursive Time-update of Filter Coefficients     199
The Steepest-descent Method     201
Convergence Rate     203
Vector-valued Adaptation Step Size     204
The LMS Filter     204
Leaky LMS Algorithm     205
Normalised LMS Algorithm     206
Summary     207
Bibliography     208
Linear Prediction Models     209
Linear Prediction Coding     210
Frequency Response of LP Models     213
Calculation of Predictor Coefficients     214
Effect of Estimation of Correlation Function on LP Model Solution     216
The Inverse Filter: Spectral Whitening     216
The Prediction Error Signal     217
Forward, Backward and Lattice Predictors     219
Augmented Equations for Forward and Backward Predictors     220
Levinson-Durbin Recursive Solution     221
Lattice Predictors     223
Alternative Formulations of Least Square Error Prediction     224
Predictor Model Order Selection     225
Short- and Long-term Predictors     226
MAP Estimation of Predictor Coefficients     228
Probability Density Function of Predictor Output      229
Using the Prior pdf of the Predictor Coefficients     230
Formant-tracking LP Models     230
Sub-band Linear Prediction Model     232
Signal Restoration using Linear Prediction Models     233
Frequency-domain Signal Restoration using Prediction Models     235
Implementation of Sub-band Linear Prediction Wiener Filters     237
Summary     238
Bibliography     238
Power Spectrum and Correlation     241
Power Spectrum and Correlation     242
Fourier Series: Representation of Periodic Signals     243
Fourier Transform: Representation of Aperiodic Signals     245
Discrete Fourier Transform     246
Time/Frequency Resolutions, the Uncertainty Principle     247
Energy-spectral Density and Power-spectral Density     248
Nonparametric Power Spectrum Estimation     249
The Mean and Variance of Periodograms     250
Averaging Periodograms (Bartlett Method)     250
Welch Method: Averaging Periodograms from Overlapped and Windowed Segments     251
Blackman-Tukey Method     252
Power Spectrum Estimation from Autocorrelation of Overlapped Segments     253
Model-based Power Spectrum Estimation      254
Maximum-entropy Spectral Estimation     255
Autoregressive Power Spectrum Estimation     257
Moving-average Power Spectrum Estimation     257
Autoregressive Moving-average Power Spectrum Estimation     258
High-resolution Spectral Estimation Based on Subspace Eigenanalysis     259
Pisarenko Harmonic Decomposition     259
Multiple Signal Classification Spectral Estimation     261
Estimation of Signal Parameters via Rotational Invariance Techniques     264
Summary     265
Bibliography     266
Interpolation     267
Introduction     268
Interpolation of a Sampled Signal     268
Digital Interpolation by a Factor of I     269
Interpolation of a Sequence of Lost Samples     271
The Factors that affect Interpolation Accuracy     273
Polynomial Interpolation     274
Lagrange Polynomial Interpolation     275
Newton Polynomial Interpolation     276
Hermite Polynomial Interpolation     278
Cubic Spline Interpolation     278
Model-based Interpolation     280
Maximum a Posteriori Interpolation     281
Least Square Error Autoregressive Interpolation      282
Interpolation based on a Short-term Prediction Model     283
Interpolation based on Long- and Short-term Correlations     286
LSAR Interpolation Error     289
Interpolation in Frequency-Time Domain     290
Interpolation using Adaptive Codebooks     293
Interpolation through Signal Substitution     294
Summary     294
Bibliography     295
Spectral Amplitude Estimation     297
Introduction     298
Spectral Representation of Noisy Signals     299
Vector Representation of the Spectrum of Noisy Signals     299
Spectral Subtraction     300
Power Spectrum Subtraction     302
Magnitude Spectrum Subtraction     303
Spectral Subtraction Filter: Relation to Wiener Filters     303
Processing Distortions     304
Effect of Spectral Subtraction on Signal Distribution     305
Reducing the Noise Variance     306
Filtering Out the Processing Distortions     307
Nonlinear Spectra] Subtraction     308
Implementation of Spectral Subtraction     310
Bayesian MMSE Spectral Amplitude Estimation     312
Application to Speech Restoration and Recognition      315
Summary     315
Bibliography     316
Impulsive Noise     319
Impulsive Noise     320
Autocorrelation and Power Spectrum of Impulsive Noise     322
Statistical Models for Impulsive Noise     323
Bernoulli-Gaussian Model of Impulsive Noise     324
Poisson-Gaussian Model of Impulsive Noise     324
A Binary-state Model of Impulsive Noise     325
Signal-to-impulsive-noise Ratio     326
Median Filters     327
Impulsive Noise Removal using Linear Prediction Models     328
Impulsive Noise Detection     328
Analysis of Improvement in Noise Detectability     330
Two-sided Predictor for Impulsive Noise Detection     331
Interpolation of Discarded Samples     332
Robust Parameter Estimation     333
Restoration of Archived Gramophone Records     334
Summary     335
Bibliography     336
Transient Noise Pulses     337
Transient Noise Waveforms     337
Transient Noise Pulse Models     339
Noise Pulse Templates     340
Autoregressive Model of Transient Noise Pulses     341
Hidden Markov Model of a Noise Pulse Process     342
Detection of Noise Pulses     342
Matched Filter for Noise Pulse Detection     343
Noise Detection based on Inverse Filtering     344
Noise Detection based on HMM     344
Removal of Noise Pulse Distortions     345
Adaptive Subtraction of Noise Pulses     345
AR-based Restoration of Signals Distorted by Noise Pulses     347
Summary     349
Bibliography     349
Echo Cancellation     351
Introduction: Acoustic and Hybrid Echoes     352
Telephone Line Hybrid Echo     353
Echo: the Sources of Delay in Telephone Networks     354
Echo Return Loss     355
Hybrid Echo Suppression     355
Adaptive Echo Cancellation     356
Echo Canceller Adaptation Methods     357
Convergence of Line Echo Canceller     358
Echo Cancellation for Digital Data Transmission     359
Acoustic Echo     360
Sub-band Acoustic Echo Cancellation     363
Multiple-input Multiple-output Echo Cancellation     365
Stereophonic Echo Cancellation Systems     365
Summary     368
Bibliography     368
Channel Equalisation and Blind Deconvolution     371
Introduction     372
The Ideal Inverse Channel Filter     373
Equalisation Error, Convolutional Noise     374
Blind Equalisation     374
Minimum- and Maximum-phase Channels     376
Wiener Equaliser     377
Blind Equalisation using the Channel Input Power Spectrum     379
Homomorphic Equalisation     380
Homomorphic Equalisation using a Bank of High-pass Filters     382
Equalisation based on Linear Prediction Models     382
Blind Equalisation through Model Factorisation     384
Bayesian Blind Deconvolution and Equalisation     385
Conditional Mean Channel Estimation     386
Maximum-likelihood Channel Estimation     386
Maximum a Posteriori Channel Estimation     386
Channel Equalisation based on Hidden Markov Models     387
MAP Channel Estimate based on HMMs     389
Implementations of HMM-based Deconvolution     390
Blind Equalisation for Digital Communications Channels     393
LMS Blind Equalisation     395
Equalisation of a Binary Digital Channel     397
Equalisation based on Higher-order Statistics     398
Higher-order Moments, Cumulants and Spectra     399
Higher-order Spectra of Linear Time-invariant Systems     401
Blind Equalisation based on Higher-order Cepstra     402
Summary     406
Bibliography     406
Speech Enhancement in Noise     409
Introduction     410
Single-input Speech-enhancement Methods     411
An Overview of a Speech-enhancement System     411
Wiener Filter for De-noising Speech     414
Spectra] Subtraction of Noise     417
Bayesian MMSE Speech Enhancement     418
Kalman Filter     419
Speech Enhancement via LP Model Reconstruction     422
Multiple-input Speech-enhancement Methods     425
Beam-forming with Microphone Arrays     427
Speech Distortion Measurements     430
Bibliography     431
Noise in Wireless Communications     433
Introduction to Cellular Communications     434
Noise, Capacity and Spectral Efficiency     436
Communications Signal Processing in Mobile Systems     438
Noise and Distortion in Mobile Communications Systems     439
Multipath Propagation of Electromagnetic Signals     440
Rake Receivers for Multipath Signals     441
Signal Fading in Mobile Communications Systems     442
Large-scale Signal Fading     443
Small-scale Fast Signal Fading     444
Smart Antennas     444
Switched and Adaptive Smart Antennas     446
Space-Time Signal Processing - Diversity Schemes     446
Summary     447
Bibliography     448
Index     449

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