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# Basic Concepts of Random Processes

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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.
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 07). Basic Concepts of Random Processes. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/lecture6_4.htm. This work is licensed under a Creative Commons License