1. Data classification^* (Deterministic vs. Random)

^* Measurement and Analysis of Random Data, Bendat (1966)

1) Deterministic data

Data can be described explicitly by a mathematical relationship.

Ex) Sinusoidal

Ex) Transient

2) Random data

Data cannot be described by explicit mathematical relationship, instead, by means of probability statement and/or statistical averages.

Ex) Ensemble of sample functions forming random process

Definitions:

For a random process {x(t)}^*, mean value μ_x(t) and autocorrelation function R_x(t,t+τ) are given by

* the symbol { } is used to denote an ensemble of sample function.

Stationary:  μ_x(t) and R_x(t,t+τ) do not vary as time t varies, i.e., μ_x(t) = μ_x and R_x(t,t+τ) = R_x(τ).

• Weakly stationary

• Strongly stationary

Ergodic: for the k^th sample function, μ_x(k) and R_x(τ,k) do not differ when computed over different sample functions.

Self-stationary: for the k^th same function, the sample properties μ_x(t,k) and R_x(t,t+τ,k) do not vary.