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| Preface | |
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| Symbols | |
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| Abbreviations | |
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| Introduction | |
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| Signals and Information | |
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| Signal Processing Methods | |
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| Transform-based Signal Processing | |
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| Model-based Signal Processing | |
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| Bayesian Signal Processing | |
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| Neural Networks | |
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| Applications of Digital Signal Processing | |
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| Adaptive Noise Cancellation | |
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| Adaptive Noise Reduction | |
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| Blind Channel Equalisation | |
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| Signal Classification and Pattern Recognition | |
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| Linear Prediction Modelling of Speech | |
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| Digital Coding of Audio Signals | |
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| Detection of Signals in Noise | |
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| Directional Reception of Waves: Beam-forming | |
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| Dolby Noise Reduction | |
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| Radar Signal Processing: Doppler Frequency Shift | |
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| Sampling and Analogue-to-digital Conversion | |
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| Sampling and Reconstruction of Analogue Signals | |
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| Quantisation | |
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| Bibliography | |
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| Noise and Distortion | |
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| Introduction | |
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| White Noise | |
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| Band-limited White Noise | |
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| Coloured Noise | |
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| Impulsive Noise | |
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| Transient Noise Pulses | |
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| Thermal Noise | |
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| Shot Noise | |
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| Electromagnetic Noise | |
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| Channel Distortions | |
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| Echo and Multipath Reflections | |
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| Modelling Noise | |
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| Additive White Gaussian Noise Model | |
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| Hidden Markov Model for Noise | |
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| Bibliography | |
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| Probability and Information Models | |
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| Introduction | |
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| Random Signals | |
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| Random and Stochastic Processes | |
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| The Space of a Random Process | |
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| Probability Models | |
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| Probability and Random Variables | |
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| Probability Mass Function | |
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| Probability Density Function | |
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| Probability Dgnsity Functions of Random Processes | |
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| Information Models | |
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| Entropy | |
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| Mutual Information | |
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| Entropy Coding | |
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| Stationary and Nonstationary Random Processes | |
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| Strict-sense Stationary Processes | |
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| Wide-sense Stationary Processes | |
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| Nonstationary Processes | |
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| Statistics (Expected Values) of a Random Process | |
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| The Mean Value | |
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| Autocorrelation | |
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| Autocovariance | |
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| Power Spectral Density | |
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| Joint Statistical Averages of Two Random Processes | |
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| Cross-correlation and Cross-covariance | |
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| Cross-power Spectral Density and Coherence | |
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| Ergodic Processes and Time-averaged Statistics | |
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| Mean-ergodic Processes | |
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| Correlation-ergodic Processes | |
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| Some Useful Classes of Random Processes | |
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| Gaussian (Normal) Process | |
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| Multivariate Gaussian Process | |
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| Mixture Gaussian Process | |
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| A Binary-state Gaussian Process | |
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| Poisson Process | |
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| Shot Noise | |
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| Poisson-Gaussian Model for Clutters and Impulsive Noise | |
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| Markov Processes | |
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| Markov Chain Processes | |
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| Gamma Probability Distribution | |
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| Rayleigh Probability Distribution | |
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| Laplacian Probability Distribution | |
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| Transformation of a Random Process | |
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| Monotonic Transformation of Random Processes | |
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| Many-to-one Mapping of Random Signals | |
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| Summary | |
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| Bibliography | |
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| Bayesian Inference | |
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| Bayesian Estimation Theory: Basic Definitions | |
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| Dynamic and Probability Models in Estimation | |
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| Parameter Space and Signal Space | |
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| Parameter Estimation and Signal Restoration | |
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| Performance Measures and Desirable Properties of Estimators | |
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| Prior and Posterior Spaces and Distributions | |
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| Bayesian Estimation | |
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| Maximum a Posteriori Estimation | |
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| Maximum-likelihood Estimation | |
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| Minimum Mean Square Error Estimation | |
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| Minimum Mean Absolute Value of Error Estimation | |
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| Equivalence of the MAP, ML, MMSE and MAVE for Gaussian Processes with Uniform Distributed Parameters | |
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| The Influence of the Prior on Estimation Bias and Variance | |
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| The Relative Importance of the Prior and the Observation | |
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| The Estimate-Maximise Method | |
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| Convergence of the EM Algorithm | |
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| Cramer-Rao Bound on the Minimum Estimator Variance | |
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| Cramer-Rao Bound for Random Parameters | |
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| Cramer-Rao Bound for a Vector Parameter | |
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| Design of Gaussian Mixture Models | |
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| EM Estimation of Gaussian Mixture Model | |
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| Bayesian Classification | |
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| Binary Classification | |
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| Classification Error | |
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| Bayesian Classification of Discrete-valued Parameters | |
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| Maximum a Posteriori Classification | |
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| Maximum-likelihood Classification | |
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| Minimum Mean Square Error Classification | |
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| Bayesian Classification of Finite State Processes | |
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| Bayesian Estimation of the Most Likely State Sequence | |
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| Modelling the Space of a Random Process | |
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| Vector Quantisation of a Random Process | |
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| Vector Quantisation using Gaussian Models | |
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| Design of a Vector Quantiser: K-means Clustering | |
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| Summary | |
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| Bibliography | |
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| Hidden Markov Models | |
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| Statistical Models for Nonstationary Processes | |
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| Hidden Markov Models | |
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| Comparison of Markov and Hidden Markov Models | |
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| A Physical Interpretation: HMMs of Speech | |
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| Hidden Markov Model as a Bayesian Model | |
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| Parameters of a Hidden Markov Model | |
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| State Observation Probability Models | |
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| State Transition Probabilities | |
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| State-Time Trellis Diagram | |
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| Training Hidden Markov Models | |
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| Forward-Backward Probability Computation | |
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| Baum-Welch Model Re-estimation | |
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| Training HMMs with Discrete Density Observation Models | |
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| HMMs with Continuous Density Observation Models | |
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| HMMs with Gaussian Mixture pdfs | |
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| Decoding of Signals using Hidden Markov Models | |
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| Viterbi Decoding Algorithm | |
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| HMMs in DNA and Protein Sequence Modelling | |
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| HMMs for Modelling Speech and Noise | |
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| Modelling Speech with HMMs | |
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| HMM-based Estimation of Signals in Noise | |
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| Signal and Noise Model Combination and Decomposition | |
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| Hidden Markov Model Combination | |
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| Decomposition of State Sequences of Signal and Noise | |
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| HMM-based Wiener Filters | |
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| Modelling Noise Characteristics | |
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| Summary | |
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| Bibliography | |
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| Least Square Error Filters | |
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| Least Square Error Estimation: Wiener Filters | |
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| Block-data Formulation of the Wiener Filter | |
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| QR Decomposition of the Least Square Error Equation | |
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| Interpretation of Wiener Filters as Projections in Vector Space | |
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| Analysis of the Least Mean Square Error Signal | |
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| Formulation of Wiener Filters in the Frequency Domain | |
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| Some Applications of Wiener Filters | |
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| Wiener Filters for Additive Noise Reduction | |
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| Wiener Filters and Separability of Signal and Noise | |
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| The Square-root Wiener Filter | |
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| Wiener Channel Equaliser | |
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| Time-alignment of Signals in Multichannel/Multisensor Systems | |
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| Implementation of Wiener Filters | |
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| The Choice of Wiener Filter Order | |
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| Improvements to Wiener Filters | |
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| Summary | |
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| Bibliography | |
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| Adaptive Filters | |
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| Introduction | |
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| State-space Kalman Filters | |
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| Derivation of the Kalman Filter Algorithm | |
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| Sample-adaptive Filters | |
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| Recursive Least Square Adaptive Filters | |
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| The Matrix Inversion Lemma | |
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| Recursive Time-update of Filter Coefficients | |
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| The Steepest-descent Method | |
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| Convergence Rate | |
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| Vector-valued Adaptation Step Size | |
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| The LMS Filter | |
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| Leaky LMS Algorithm | |
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| Normalised LMS Algorithm | |
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| Summary | |
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| Bibliography | |
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| Linear Prediction Models | |
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| Linear Prediction Coding | |
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| Frequency Response of LP Models | |
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| Calculation of Predictor Coefficients | |
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| Effect of Estimation of Correlation Function on LP Model Solution | |
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| The Inverse Filter: Spectral Whitening | |
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| The Prediction Error Signal | |
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| Forward, Backward and Lattice Predictors | |
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| Augmented Equations for Forward and Backward Predictors | |
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| Levinson-Durbin Recursive Solution | |
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| Lattice Predictors | |
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| Alternative Formulations of Least Square Error Prediction | |
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| Predictor Model Order Selection | |
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| Short- and Long-term Predictors | |
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| MAP Estimation of Predictor Coefficients | |
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| Probability Density Function of Predictor Output | |
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| Using the Prior pdf of the Predictor Coefficients | |
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| Formant-tracking LP Models | |
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| Sub-band Linear Prediction Model | |
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| Signal Restoration using Linear Prediction Models | |
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| Frequency-domain Signal Restoration using Prediction Models | |
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| Implementation of Sub-band Linear Prediction Wiener Filters | |
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| Summary | |
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| Bibliography | |
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| Power Spectrum and Correlation | |
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| Power Spectrum and Correlation | |
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| Fourier Series: Representation of Periodic Signals | |
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| Fourier Transform: Representation of Aperiodic Signals | |
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| Discrete Fourier Transform | |
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| Time/Frequency Resolutions, the Uncertainty Principle | |
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| Energy-spectral Density and Power-spectral Density | |
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| Nonparametric Power Spectrum Estimation | |
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| The Mean and Variance of Periodograms | |
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| Averaging Periodograms (Bartlett Method) | |
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| Welch Method: Averaging Periodograms from Overlapped and Windowed Segments | |
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| Blackman-Tukey Method | |
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| Power Spectrum Estimation from Autocorrelation of Overlapped Segments | |
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| Model-based Power Spectrum Estimation | |
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| Maximum-entropy Spectral Estimation | |
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| Autoregressive Power Spectrum Estimation | |
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| Moving-average Power Spectrum Estimation | |
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| Autoregressive Moving-average Power Spectrum Estimation | |
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| High-resolution Spectral Estimation Based on Subspace Eigenanalysis | |
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| Pisarenko Harmonic Decomposition | |
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| Multiple Signal Classification Spectral Estimation | |
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| Estimation of Signal Parameters via Rotational Invariance Techniques | |
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| Summary | |
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| Bibliography | |
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| Interpolation | |
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| Introduction | |
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| Interpolation of a Sampled Signal | |
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| Digital Interpolation by a Factor of I | |
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| Interpolation of a Sequence of Lost Samples | |
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| The Factors that affect Interpolation Accuracy | |
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| Polynomial Interpolation | |
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| Lagrange Polynomial Interpolation | |
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| Newton Polynomial Interpolation | |
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| Hermite Polynomial Interpolation | |
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| Cubic Spline Interpolation | |
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| Model-based Interpolation | |
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| Maximum a Posteriori Interpolation | |
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| Least Square Error Autoregressive Interpolation | |
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| Interpolation based on a Short-term Prediction Model | |
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| Interpolation based on Long- and Short-term Correlations | |
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| LSAR Interpolation Error | |
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| Interpolation in Frequency-Time Domain | |
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| Interpolation using Adaptive Codebooks | |
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| Interpolation through Signal Substitution | |
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| Summary | |
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| Bibliography | |
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| Spectral Amplitude Estimation | |
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| Introduction | |
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| Spectral Representation of Noisy Signals | |
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| Vector Representation of the Spectrum of Noisy Signals | |
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| Spectral Subtraction | |
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| Power Spectrum Subtraction | |
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| Magnitude Spectrum Subtraction | |
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| Spectral Subtraction Filter: Relation to Wiener Filters | |
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| Processing Distortions | |
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| Effect of Spectral Subtraction on Signal Distribution | |
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| Reducing the Noise Variance | |
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| Filtering Out the Processing Distortions | |
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| Nonlinear Spectra] Subtraction | |
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| Implementation of Spectral Subtraction | |
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| Bayesian MMSE Spectral Amplitude Estimation | |
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| Application to Speech Restoration and Recognition | |
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| Summary | |
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| Bibliography | |
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| Impulsive Noise | |
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| Impulsive Noise | |
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| Autocorrelation and Power Spectrum of Impulsive Noise | |
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| Statistical Models for Impulsive Noise | |
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| Bernoulli-Gaussian Model of Impulsive Noise | |
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| Poisson-Gaussian Model of Impulsive Noise | |
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| A Binary-state Model of Impulsive Noise | |
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| Signal-to-impulsive-noise Ratio | |
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| Median Filters | |
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| Impulsive Noise Removal using Linear Prediction Models | |
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| Impulsive Noise Detection | |
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| Analysis of Improvement in Noise Detectability | |
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| Two-sided Predictor for Impulsive Noise Detection | |
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| Interpolation of Discarded Samples | |
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| Robust Parameter Estimation | |
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| Restoration of Archived Gramophone Records | |
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| Summary | |
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| Bibliography | |
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| Transient Noise Pulses | |
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| Transient Noise Waveforms | |
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| Transient Noise Pulse Models | |
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| Noise Pulse Templates | |
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| Autoregressive Model of Transient Noise Pulses | |
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| Hidden Markov Model of a Noise Pulse Process | |
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| Detection of Noise Pulses | |
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| Matched Filter for Noise Pulse Detection | |
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| Noise Detection based on Inverse Filtering | |
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| Noise Detection based on HMM | |
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| Removal of Noise Pulse Distortions | |
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| Adaptive Subtraction of Noise Pulses | |
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| AR-based Restoration of Signals Distorted by Noise Pulses | |
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| Summary | |
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| Bibliography | |
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| Echo Cancellation | |
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| Introduction: Acoustic and Hybrid Echoes | |
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| Telephone Line Hybrid Echo | |
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| Echo: the Sources of Delay in Telephone Networks | |
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| Echo Return Loss | |
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| Hybrid Echo Suppression | |
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| Adaptive Echo Cancellation | |
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| Echo Canceller Adaptation Methods | |
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| Convergence of Line Echo Canceller | |
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| Echo Cancellation for Digital Data Transmission | |
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| Acoustic Echo | |
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| Sub-band Acoustic Echo Cancellation | |
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| Multiple-input Multiple-output Echo Cancellation | |
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| Stereophonic Echo Cancellation Systems | |
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| Summary | |
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| Bibliography | |
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| Channel Equalisation and Blind Deconvolution | |
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| Introduction | |
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| The Ideal Inverse Channel Filter | |
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| Equalisation Error, Convolutional Noise | |
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| Blind Equalisation | |
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| Minimum- and Maximum-phase Channels | |
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| Wiener Equaliser | |
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| Blind Equalisation using the Channel Input Power Spectrum | |
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| Homomorphic Equalisation | |
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| Homomorphic Equalisation using a Bank of High-pass Filters | |
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| Equalisation based on Linear Prediction Models | |
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| Blind Equalisation through Model Factorisation | |
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| Bayesian Blind Deconvolution and Equalisation | |
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| Conditional Mean Channel Estimation | |
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| Maximum-likelihood Channel Estimation | |
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| Maximum a Posteriori Channel Estimation | |
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| Channel Equalisation based on Hidden Markov Models | |
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| MAP Channel Estimate based on HMMs | |
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| Implementations of HMM-based Deconvolution | |
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| Blind Equalisation for Digital Communications Channels | |
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| LMS Blind Equalisation | |
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| Equalisation of a Binary Digital Channel | |
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| Equalisation based on Higher-order Statistics | |
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| Higher-order Moments, Cumulants and Spectra | |
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| Higher-order Spectra of Linear Time-invariant Systems | |
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| Blind Equalisation based on Higher-order Cepstra | |
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| Summary | |
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| Bibliography | |
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| Speech Enhancement in Noise | |
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| Introduction | |
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| Single-input Speech-enhancement Methods | |
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| An Overview of a Speech-enhancement System | |
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| Wiener Filter for De-noising Speech | |
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| Spectra] Subtraction of Noise | |
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| Bayesian MMSE Speech Enhancement | |
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| Kalman Filter | |
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| Speech Enhancement via LP Model Reconstruction | |
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| Multiple-input Speech-enhancement Methods | |
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| Beam-forming with Microphone Arrays | |
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| Speech Distortion Measurements | |
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| Bibliography | |
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| Noise in Wireless Communications | |
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| Introduction to Cellular Communications | |
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| Noise, Capacity and Spectral Efficiency | |
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| Communications Signal Processing in Mobile Systems | |
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| Noise and Distortion in Mobile Communications Systems | |
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| Multipath Propagation of Electromagnetic Signals | |
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| Rake Receivers for Multipath Signals | |
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| Signal Fading in Mobile Communications Systems | |
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| Large-scale Signal Fading | |
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| Small-scale Fast Signal Fading | |
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| Smart Antennas | |
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| Switched and Adaptive Smart Antennas | |
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| Space-Time Signal Processing - Diversity Schemes | |
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| Summary | |
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| Bibliography | |
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| Index | |