Advanced Signal Processing and Digital Noise Reduction

1 Introduction.- 1.1 Signals and Information.- 1.2 Signal Processing Methods.- 1.3 Applications of Digital Signal Processing.- 1.4 Sampling and Analog to Digital Conversion.- 2 Stochastic Processes.- 2.1 Random Signals and Stochastic Processes.- 2.2 Probabilistic Models of a Random Process.- 2.3 Stationary and Nonstationary Random Processes.- 2.4 Expected Values of a Stochastic Process.- 2.5 Some Useful Classes of Random Processes.- 2.6 Transformation of a Random Process.- Summary.- 3 Bayesian Estimation and Classification.- 3.1 Estimation Theory: Basic Definitions.- 3.2 Bayesian Estimation.- 3.3 Estimate-Maximise (EM) Method.- 3.4 Cramer-Rao Bound on the Minimum Estimator Variance.- 3.5 Bayesian Classification.- 3.6 Modelling the Space of a Random Signal.- Summary.- 4 Hidden Markov Models.- 4.1 Statistical Models for Nonstationary Processes.- 4.2 Hidden Markov Models.- 4.3 Training Hidden Markov Models.- 4.4 Decoding of Signals Using Hidden Markov Models.- 4.5 HMM-based Estimation of Signals in Noise.- Summary.- 5 Wiener Filters.- 5.1 Wiener Filters: Least Squared Error Estimation.- 5.2 Block-data Formulation of the Wiener Filter.- 5.3 Vector Space Interpretation of Wiener Filters.- 5.4 Analysis of the Least Mean Squared Error Signal.- 5.5 Formulation of Wiener Filter in Frequency Domain.- 5.6 Some Applications of Wiener Filters.- Summary.- 6 Kalman and Adaptive Least Squared Error Filters.- 6.1 State-space Kalman Filters.- 6.2 Sample Adaptive Filters.- 6.3 Recursive Least Squares (RLS) Adaptive Filters.- 6.4 The Steepest Descent Method.- 6.5 The LMS Adaptation Method.- Summary.- 7 Linear Prediction Models.- 7.1 Linear Prediction Coding.- 7.2 Forward, Backward and Lattice Predictors.- 7.3 Short-term and Long-term Predictors.- 7.4 MAP Estimation of Predictor Coefficients.- 7.5 Signal Restoration Using Linear Prediction Models.- Summary.- 8 Power Spectrum Estimation.- 8.1 Fourier Transform, Power Spectrum and Correlation.- 8.2 Non-parametric Power Spectrum Estimation.- 8.3 Model-based Power Spectrum Estimation.- 8.4 High Resolution Spectral Estimation Based on Subspace Eigen Analysis.- Summary.- 9 Spectral Subtraction.- 9.1 Spectral Subtraction.- 9.2 Processing Distortions.- 9.3 Non-linear Spectral Subtraction.- 9.4 Implementation of Spectral Subtraction.- Summary.- 10 Interpolation.- 10.1 Introduction.- 10.2 Polynomial Interpolation.- 10.3 Statistical Interpolation.- Summary.- 11 Impulsive Noise.- 11.1 Impulsive Noise.- 11.2 Stochastic Models for Impulsive Noise.- 11.3 Median Filters.- 11.4 Impulsive Noise Removal Using Linear Prediction Models.- 11.5 Robust Parameter Estimation.- 11.6 Restoration of Archived Gramophone Records.- Summary.- 12 Transient Noise.- 12.1 Transient Noise Waveforms.- 12.2 Transient Noise Pulse Models.- 12.3 Detection of Noise Pulses.- 12.4 Removal of Noise Pulse Distortions.- Summary.- 13 Echo Cancellation.- 13.1 Telephone Line Echoes.- 13.2 Adaptive Echo Cancellation.- 13.3 Acoustic Feedback Coupling.- 13.4 Sub-band Acoustic Echo Cancellation.- Summary.- 14 Blind Deconvolution and Channel Equalisation.- 14.1 Introduction.- 14.2 Blind Equalisation Using Channel Input Power Spectrum.- 14.3 Equalisation Based on Linear Prediction Models.- 14.4 Bayesian Blind Deconvolution and Equalisation.- 14.5 Blind Equalisation for Digital Communication Channels.- 14.6 Equalisation Based on Higher-Order Statistics.- Summary.- Frequently used Symbols and Abbreviations.