Symbols.

Abbreviations.

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. NOISE AND DISTORTION.

2.1 Introduction.

2.2 White Noise.

2.3 Coloured Noise.

2.4 Impulsive Noise.

2.5 Transient Noise Pulses.

2.6 Thermal Noise.

2.7 Shot Noise.

2.8 Electromagnetic Noise.

2.9 Channel Distortions.

2.10 Echo and Multi-path Reflections.

2.11 Modelling Noise.

3. PROBABILITY & INFORMATION MODELS.

3.1 Introduction: Probability and Information Models.

3.2 Random Signals.

3.3 Probability Models.

3.4 Information Models.

3.5 Stationary and Non-Stationary Random Processes.

3.6 Statistics (Expected Values) of a Random Process.

3.7 Some Useful Classes of Random Processes.

3.8 Transformation of a Random Process.

3.9 Summary.

4. BAYESIAN INFERENCE.

4.1 Bayesian Estimation Theory: Basic Definitions.

4.2 Bayesian Estimation.

4.3 The Estimate–Maximise (EM) Method.

4.4 Cramer–Rao Bound on the Minimum Estimator Variance.

4.5 Design of Gaussian Mixture Models.

4.6 Bayesian Classification .

4.7 Modelling the Space of a Random Process.

4.8 Summary .

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.

5.6 HMMs for Modelling Speech and Noise.

5.7 Summary.

6. LEAST SQUARE ERROR FILTERS.

6.1 Least Square Error Estimation: Wiener Filter.

6.2 Block-Data Formulation of the Wiener Filter.

6.3 Interpretation of Wiener Filter 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.

7. ADAPTIVE FILTERS.

7.1 Introduction.

7.2 State-Space Kalman Filters.

7.3 Sample Adaptive Filters.

7.4 Recursive Least Square (RLS) Adaptive Filters.

7.5 The Steepest-Descent Method.

7.6 LMS Filter.

7.7 Summary.

8. LINEAR PREDICTION MODELS.

8.1 Linear Prediction Coding.

8.2 Forward, Backward and Lattice Predictors.

8.3 Short-Term and Long-Term Predictors.

8.4 MAP Estimation of Predictor Coefficients.

8.5 Formant-Tracking LP Models.

8.6 Sub-Band Linear Prediction Model.

8.7 Signal Restoration Using Linear Prediction Models.

8.8 Summary.

9. POWER SPECTRUM AND CORRELATION.

9.1 Power Spectrum and Correlation.

9.2 Fourier Series: Representation of Periodic Signals.

9.3 Fourier Transform: Representation of Aperiodic Signals.

9.4 Non-Parametric Power Spectrum Estimation.

9.5 Model-Based Power Spectrum Estimation.

9.6 High-Resolution Spectral Estimation Based on Subspace Eigen-Analysis.

9.7 Summary.

10. INTERPOLATION.

10.1 Introduction.

10.2 Polynomial Interpolation.

10.3 Model-Based Interpolation.

10.4 Summary.

11. SPECTRAL AMPLITUDE ESTIMATION.

11.1. Introduction.

11.2 Spectral Subtraction.

11.3 Bayesian MMSE Spectral Amplitude Estimation.

11.4 Application to Speech Restoration and Recognition.

11.5 Summary.

12. IMPULSIVE NOISE.

12.1 Impulsive Noise.

12.2 Statistical Models for Impulsive Noise.

12.3 Median Filters.

12.4 Impulsive Noise Removal Using Linear Prediction Models.

12.5 Robust Parameter Estimation.

12.6 Restoration of Archived Gramophone Records.

12.7 Summary.

13. TRANSIENT NOISE PULSES.

13.1 Transient Noise Waveforms.

13.2 Transient Noise Pulse Models.

13.3 Detection of Noise Pulses.

13.4 Removal of Noise Pulse Distortions.

13.5 Summary.

14. ECHO CANCELLATION.

14.1 Introduction: Acoustic and Hybrid Echo.

14.2 Telephone Line Hybrid Echo.

14.3 Hybrid Echo Suppression.

14.4 Adaptive Echo Cancellation.

14.5 Acoustic Echo.

14.6 Sub-Band Acoustic Echo Cancellation.

14.7 Multi-Input Multi-Output (MIMO) Echo Cancellation.

14.8 Summary.

15. CHANNEL EQUALIZATION & BLIND DECONVOLUTION.

15.1 Introduction.

15.2 Blind Equalization Using Channel Input Power Spectrum.

15.3 Equalization Based on Linear Prediction Models.

15.4 Bayesian Blind Deconvolution and Equalization.

15.5 Blind Equalization for Digital Communication Channels.

15.6 Equalization Based on Higher-Order Statistics.

15.7 Summary.

16. SPEECH ENHANCEMENT IN NOISE.

16.1 Introduction.16.2 Single-Input Speech Enhancement Methods.

16.3 Multi-Input Speech Enhancement Methods.

16.4 Speech Distortion Measurements.

17. NOISE IN WIRELESS COMMUNICATION.

17.1 Introduction to Cellular Communication.

17.2 Noise, Capacity and Spectral Efficiency.

17.3 Communication Signal Processing in Mobile Systems.

17.4 Noise and Distortion in Mobile Communication Systems.

17.5 Smart Antennas.

17.6 Summary.

Bibliography.

Index.