# Basic Concepts of Random Processes

Definitions :: Ergodicity :: Autocorrelations :: Sinusoidal :: Poisson :: Gaussian :: Properties :: Spectra :: Cases :: Random :: Independent

## A Sinusoidal Process

Let
. Assume
and
are independent r.v.s, with
and
. Define
by

where is a known constant.

A typical realization is a sinusoid.

This is an example of a
**
deterministic
**
random process, that is, a
random process determined by random parameters.

We observe that this process is ergodic in the mean -- a time average is equal to the ensemble average.

We observe that depends only on the time difference . Hence, the r.p. is WSS. Let . We can write

Checking the properties, observe that we have a (local) maximum at , and that the function is symmetric.