Stochastic Processes

Resources: 1.2.4, 12.1

We are used to Deterministic signals, aka signals we know given an input. How about for example a coinflip? Or random signals.

Definitions

Stochastic signal

A sequence of random numbers

Link to original

Formulas

Mean of a stochastic process:

• Average over all realizations of the process $m_x[n]=E(X[n])$

Crosscovariance: (very similar to Crosscorrelation)

Notation

$X[n,S]$ is the ensemble of possible waveforms, where $n$ represents time, and $S=s_1,s_2,\dots$ represents the set of all possible functions. This means that a single waveform in ensemble is denoted by $x[n,s]=x[n]$