Note for Multimedia and Signal Coding - MSC By JNTU Heroes

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Multimedia Signal Processing Theory and Applications in Speech, Music and Communications Provided By: JNTU World (www.alljntuworld.in)

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Contents Preface xiii Acknowledgement xvii Symbols xix Abbreviations Part I xxiii Basic Digital Signal Processing 1 1 Introduction 1.1 Signals and Information 1.2 Signal Processing Methods 1.3 Applications of Digital Signal Processing 1.4 Summary 3 3 5 8 23 2 Fourier Analysis and Synthesis 2.1 Introduction 2.2 Fourier Series: Representation of Periodic Signals 2.3 Fourier Transform: Representation of Nonperiodic Signals 2.4 Discrete Fourier Transform 2.5 Short-Time Fourier Transform 2.6 Fast Fourier Transform (FFT) 2.7 2-D Discrete Fourier Transform (2-D DFT) 2.8 Discrete Cosine Transform (DCT) 2.9 Some Applications of the Fourier Transform 2.10 Summary 25 25 27 33 48 57 59 65 66 68 74 3 z-Transform 3.1 Introduction 3.2 Derivation of the z-Transform 79 79 81

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viii 3.3 3.4 3.5 3.6 3.7 3.8 CONTENTS The z-Plane and the Unit Circle Properties of z-Transform z-Transfer Function, Poles (Resonance) and Zeros (Anti-resonance) z-Transform of Analysis of Exponential Transient Signals Inverse z-Transform Summary 83 88 91 100 104 106 4 Digital Filters 4.1 Introduction 4.2 Linear Time-Invariant Digital Filters 4.3 Recursive and Non-Recursive Filters 4.4 Filtering Operation: Sum of Vector Products, A Comparison of Convolution and Correlation 4.5 Filter Structures: Direct, Cascade and Parallel Forms 4.6 Linear Phase FIR Filters 4.7 Design of Digital FIR Filter-banks 4.8 Quadrature Mirror Sub-band Filters 4.9 Design of Infinite Impulse Response (IIR) Filters by Pole–zero Placements 4.10 Issues in the Design and Implementation of a Digital Filter 4.11 Summary 111 111 113 115 5 Sampling and Quantisation 5.1 Introduction 5.2 Sampling a Continuous-Time Signal 5.3 Quantisation 5.4 Sampling Rate Conversion: Interpolation and Decimation 5.5 Summary 155 155 158 162 166 171 Part II 173 Model-Based Signal Processing 117 119 122 136 139 145 148 148 6 Information Theory and Probability Models 6.1 Introduction: Probability and Information Models 6.2 Random Processes 6.3 Probability Models of Random Signals 6.4 Information Models 6.5 Stationary and Non-Stationary Random Processes 6.6 Statistics (Expected Values) of a Random Process 6.7 Some Useful Practical Classes of Random Processes 6.8 Transformation of a Random Process 6.9 Search Engines: Citation Ranking 6.10 Summary 175 176 177 182 189 199 202 212 225 230 231 7 Bayesian Inference 7.1 Bayesian Estimation Theory: Basic Definitions 7.2 Bayesian Estimation 233 233 242

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CONTENTS 7.3 7.4 7.5 7.6 7.7 7.8 8 Least 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 ix Expectation Maximisation Method Cramer–Rao Bound on the Minimum Estimator Variance Design of Gaussian Mixture Models (GMM) Bayesian Classification Modelling the Space of a Random Process Summary 255 257 260 263 270 273 Square Error, Wiener–Kolmogorov Filters Least Square Error Estimation: Wiener–Kolmogorov Filter Block-Data Formulation of the Wiener Filter Interpretation of Wiener Filter as Projection in Vector Space Analysis of the Least Mean Square Error Signal Formulation of Wiener Filters in the Frequency Domain Some Applications of Wiener Filters Implementation of Wiener Filters Summary 275 275 280 9 Adaptive Filters: Kalman, RLS, LMS 9.1 Introduction 9.2 State-Space Kalman Filters 9.3 Sample Adaptive Filters 9.4 Recursive Least Square (RLS) Adaptive Filters 9.5 The Steepest-Descent Method 9.6 LMS Filter 9.7 Summary 282 284 285 286 292 294 297 297 299 307 309 313 317 321 10 Linear Prediction Models 10.1 Linear Prediction Coding 10.2 Forward, Backward and Lattice Predictors 10.3 Short-Term and Long-Term Predictors 10.4 MAP Estimation of Predictor Coefficients 10.5 Formant-Tracking LP Models 10.6 Sub-Band Linear Prediction Model 10.7 Signal Restoration Using Linear Prediction Models 10.8 Summary 323 323 332 339 341 343 344 345 350 11 Hidden Markov Models 11.1 Statistical Models for Non-Stationary Processes 11.2 Hidden Markov Models 11.3 Training Hidden Markov Models 11.4 Decoding Signals Using Hidden Markov Models 11.5 HMM in DNA and Protein Sequences 11.6 HMMs for Modelling Speech and Noise 11.7 Summary 353 353 355 361 367 371 372 378