Advanced Digital Signal Processing and Noise Reduction 4e

SAEED V. VASEGHI, Brunel University, UK

Contents Symbols Abbreviations 1 Introduction 1.1 Signals, Noise and Information 1.2 Signal Processing Methods 1.3 Applications of Digital Signal Processing 1.4 A Review of Sampling and Quantisation 1.5 Summary Bibliography 2 Noise and Distortion 2.1 Introduction 2.2 White Noise 2.3 Coloured Noise; Pink Noise and Brown Noise 2.4 Impulsive and Click Noise 2.5 Impulsive and Click Noise 2.6 Thermal Noise 2.7 Shot Noise 2.8 Flicker (I/f) Noise 2.9 Burst Noise 2.10 Electromagnetic (Radio) Noise 2.11 Channel Distortions 2.12 Echo and Multi-path Reflections 2.13 Modelling Noise 2.14 Summary Bibliography 3 Information Theory and Probability Models 3.1 Introduction: Probability and Information Models 3.2 Random Processes 3.3 Probability Models 3.4 Information Models 3.5 Stationary and Non-stationary Processes 3.6 Expected Values of a Process 3.7 Some Useful Classes of Random Processes 3.8 Transformation of a Random Process 3.9 Search Engines: Citation Ranking 3.10 Summary Bibliography 4 Baseyian Inference 4.1 Bayesian Estimation Theory: Basic Definitions 4.2 Bayesian Estimation 4.3 The Estimate-Maximise Method 4.4 Cramer-Rao Bound on the Minimum Estimator Variance 4.5 Design of Gaussian Mixture Models 4.6 Bayesian Classification 4.7 Modeling the Space of a Random Process 4.8 Summary Bibliography 5 Hidden Markov Models 5.1 Statistical Models for Non-Stationary Processes 5.2 Hidden Markov Models 5.3 Training Hidden Markov Models 5.4 Decoding of Signals Using Hidden Markov Models 5.5 HMM In DNA and Protein Sequence Modelling 5.6 HMMs for Modelling Speech and Noise 5.7 Summary Bibliography 6 Least Square Error Wiener-Kolmogorov Filters 6.1 Least Square Error Estimation: Wiener-Kolmogorov Filter 6.2 Block-Data Formulation of the Wiener Filter 6.3 Interpretation of Wiener Filters as Projection in Vector Space 6.4 Analysis of the Least Mean Square Error Signal 6.5 Formulation of Wiener Filters in the Frequency Domain 6.6 Some Applications of Wiener Filters 6.7 Implementation of Wiener Filters 6.8 Summary Bibliography 7 Adaptive Filters, Kalman, RLS, LMS 7.1 Introduction 7.2 State-Space Kalman Filter 7.3 Extended Kalman Filter 7.4 Unscented Kalman Filter 7.5 Sample-Adaptive Filters 7.6 Recursive Least Square(RLS) Adaptive Filters 7.7 The Steepest-Descent Method 7.8 The LMS Filter 7.9 Summary Bibliography 8 Linear Prediction Models 8.1 Linear Prediction Coding 8.2 Forward, Backward and Lattice Predictors 8.3 Short-term and Long-Term Linear Predictors 8.4 MAP Estimation of Predictor Coefficients 8.5 Formant-Tracking LP Models 8.6 Sub-Band Linear Prediction 8.7 .i.Signal Restoration Using Linear Prediction Models 8.8 Summary Bibliography 9 Eigenvalue Analysis and Principal Component Analysis 9.1 Introduction 9.2 Eigen Analysis 9.3 Principal Component Analysis 9.4 Summary Bibliography 10 Power Spectrum Analysis 10.1 Power Spectrum and Correlation 10.2 Fourier Series: Representation of Periodic Signals 10.3.3 Energy-Spectral Density and Power-Spectral Density 10.3 Fourier Transform: Representation of Aperiodic Signals 10.4 Non-Parametric Power Spectrum Estimation 10.5 Model-Based Power Spectral Estimation 10.6 High Resolution Spectral Estimation Based on Subspace Eigen-Analysis 10.7 Summary Bibliography 11. Interpolation - Replacement of Lost Samples 11.1 Introduction 11.2 Model-Based Interpolation 11.3 Model-Based Interpolation 11.4 Summary Bibliography 12 Signal Enhancement via Spectral Amplitude Estimation 12.1Introduction 12.2 Spectral Representation of Noisy Signals 12.3 Vector Representation of Spectrum of Noisy Signals 12.4 Spectral Subtraction 12.5 Bayesian MMSE Spectral Amplitude Estimation 12.6 Estimation of Signal to Noise Ratios 12.7 Application to Speech Restoration and Recognition 12.8 Summary Bibliography 13 Impulsive Noise: Modelling, Detection and Removal 13.1 Impulsive Noise 13.2 Autocorrelation and Power Spectrum of Impulsive Noise 13.3 Probability Models for Impulsive Noise 13.4 Impulse contamination, Signal to Impulsive Noise Ratio 13.5 Median Filters 13.6 Impulsive Noise Removal Using Linear Prediction Models 13.7 Robust Parameter Estimation 13.8 Restoration of Archived Gramophone Records 13.9 Summary Bibliography 14 Transient Noise Pulses 14.1 Transient Noise Waveforms 14.2 Transient Noise Pulse Models 14.3 Detection of Noise Pulses 14.4 Removal of Noise Pulse Distortions 14.5 Summary Bibliography 15 Echo Cancellation 15.1 Introduction: Acoustic and Hybrid.i.Hybrid Echoes 15.2 Echo Return Time: The Sources of Delay in Communication Networks 15.3 Telephone Line Hybrid Echo 15.4 Hybrid Echo Suppression 15.5 .i.Adaptive Echo Cancellation 15.6 Acoustic .i.Echo 15.7 .i.Sub-band Acoustic Echo Cancellation 15.8 .i. Echo Cancellation with Linear Prediction Pre-whitening 15.9 Multiple-Input Multiple-Output (MIMO) Acoustic Echo Cancellation 15.10 Summary Bibliography 16 Channel Equalisation and Blind Deconvolution 16.1 Introduction 16.2 Blind-Deconvolution Using Channel Input Power Spectrum 16.3 Equalisation Based on Linear Prediction Models 16.4 Bayesian Blind Deconvolution and Equalisation 16.5 Blind Equalisation for Digital Communication Channels 16.6 Equalisation Based on Higher-Order Statistics 16.7 Summary 16.8 Bibliography 17 Speech Enhancement: Noise Reduction, Bandwidth Extension and Packet Replacement 17.1 An Overview of Speech Enhancement in Noise 17.2 Single-Input Speech Enhancement Methods 17.3 Speech Bandwidth Extension 17.4 Interpolation of Lost Speech Segments 17.5 Multiple-Input Speech Enhancement Methods 17.6 Speech Distortion Measurements 17.7 Summary 17.8 Bibliography 18 Multiple-Input Multiple-Output Systems, Independent Component Analysis 18.1 Introduction 18.2 MIMO Signal Propagation and Mixing Models 18.3 Independent Component Analysis 18.4 Summary Bibliography 19 Signal Processing in Mobile Communication 19.1 Introduction to Cellular Communication 19.2 Communication Signal Processing in Mobile Systems 19.3 Noise, Capacity and Spectral Efficiency 19.4 Multi-path and Fading in Mobile Communication 19.5 Smart Beam-forming Antennas 19.6 Summary Bibliography Index