Digital Signal and Image Processing using Matlab 2 – 2nd edition

Foreword ix
<p>Notations and Abbreviations xiii</p>
<p>1 Mathematical Concepts 1</p>
<p>1.1 Basic concepts on probability 1</p>
<p>1.2 Conditional expectation 9</p>
<p>1.3 Projection theorem 10</p>
<p>1.4 Gaussianity 13</p>
<p>1.5 Random variable transformation 18</p>
<p>1.6 Fundamental statistical theorems 21</p>
<p>1.7 Other important probability distributions 23</p>
<p>2 Statistical Inferences 25</p>
<p>2.1 Statistical model 25</p>
<p>2.2 Hypothesis tests 27</p>
<p>2.3 Statistical estimation 41</p>
<p>3 Monte–Carlo Simulation 85</p>
<p>3.1 Fundamental theorems 85</p>
<p>3.2 Stating the problem 86</p>
<p>3.3 Generating random variables 88</p>
<p>3.4 Variance reduction 99</p>
<p>4 Second Order Stationary Process 107</p>
<p>4.1 Statistics for empirical correlation 107</p>
<p>4.2 Linear prediction of WSS processes 111</p>
<p>4.3 Non–parametric spectral estimation of WSS processes 124</p>
<p>5 Inferences on HMM 139</p>
<p>5.1 Hidden Markov Models (HMM) 130</p>
<p>5.2 Inferences on HMM 142</p>
<p>5.3 Gaussian linear case: the Kalman filter 143</p>
<p>5.4 Discrete finite Markov case 152</p>
<p>6 Selected Topics 163</p>
<p>6.1 High resolution methods 163</p>
<p>6.2 Digital Communications 186</p>
<p>6.3 Linear equalization and the Viterbi algorithm 211</p>
<p>6.4 Compression 220</p>
<p>7 Hints and Solutions 235</p>
<p>H1 Mathematical concepts 235</p>
<p>H2 Statistical inferences 237</p>
<p>H3 Monte–Carlo simulation 269</p>
<p>H4 Second order stationary process 283</p>
<p>H5 Inferences on HMM 283</p>
<p>H6 Selected Topics 300</p>
<p>8 Appendices 317</p>
<p>A1 Miscellaneous functions 317</p>
<p>A2 Statistical functions 318</p>
<p>Bibliography 329</p>
<p>Index 333</p>