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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 | |