Probability and Stochastic Processes

List of Figures List of Tables 1 Principles of Communications with Focus on AM 2 Baseband Digital Modulation with Focus on PAM 3 Passband Digital Modulation with Focus on QAM 4 Channels: Modeling, Simulating and Mitigating their Effects 5 Optimal Receivers and Probability of Error for AWGN 6 Multicarrier systems A Useful Mathematics A.1 Euler’s Equation A.2 Trigonometry A.3 Manipulating Complex Numbers and Rational Functions A.4 Manipulating Complex Exponentials A.5 Geometric Series A.6 Sum of Squares A.7 Summations and Integrals A.8 Partial Fraction Decomposition A.9 Calculus A.10 Sinc Function A.11 Rectangular Integration Defining Normalization Factors A.12 Linear Algebra A.13 Gram-Schmidt orthonormalization procedure A.14 Principal component analysis (PCA) A.15 Fourier Analysis: Properties A.16 Fourier Analysis: Pairs A.17 Probability and Stochastic Processes A.18 Probability A.19 Stochastic Processes A.20 Estimation Theory A.21 One-dimensional Linear Prediction Over Time A.22 Advanced: Vector Prediction Exploring Spatial Correlation A.23 Spatial Whitening Applied to Interference Mitigation A.24 Space-Time Prediction A.25 Non-linear Decorrelation A.26 Noise Prediction and DFE A.27 Decibel (dB) and Related Definitions A.28 Insertion Loss and Insertion Frequency Response A.29 Discrete and Continuous-Time Impulses A.30 System Properties A.31 Fixed and Floating-Point Number Representations B Useful Softwares and Programming Tricks C Analog and Digital Signals D Transforms and Signal Representation E Analog and Digital Systems F Spectral Estimation Techniques

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A.17 Probability and Stochastic Processes

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