Modern Digital Signal Processing

Statistical Random

  1. Linear Processing
  • Fundamental
    • Statistical Foundation
    • Orthogonal
    • Orthogonalization
  • Typical
    • Wiener, Kalman
  • Extension
    • SVM, Kernel, Regularization
  1. Adaptive Processing
  • Adaptive Filter, LMS, RLS
  1. Spectral Processing
  • Direct(Non-Parametric), Filter Banks

1950’s~1980’s Linear, Orthogonal, Stationary, Gaussian

Chapter 1

Review of Probability Theory

概率的定义：

Uncertainty $\rightarrow$ Statistical Experiment $\rightarrow$ Sample Points $\rightarrow$ Sample Space $(\Omega)$ $\rightarrow$ Possibility(Prior)

$\rightarrow$ Probability(概率) $P: X^\Omega\rightarrow[0,1]$

概率与统计

Data $\longrightarrow$ Model $\longrightarrow$ Decision (Big Data: Data $\longrightarrow$ Decision)
   $\Downarrow$        $\Downarrow$
  Statistics   Probability

Random Variables: $X:\Omega\rightarrow R$ (Quantization)

$P(X=x)=P({w\in\Omega|Z(w)=x})$

Discrete: $\Omega = {w_1,w_2,\dots,w_n}$.   分布列：$P(X=x_k)=P_k$

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