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# Basic Concepts of Random Processes

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

## Cases when does not have a transform

We examine this and other cases that are WSS but do not have a Fourier transform (in the conventional sense).

1. Suppose . Then is continuous and is the autocorrelation function of a WSS r.p. if and only if there is a c.d.f. satisfying such that

This transform is called the Fourier-Stieltjes transform.
2. Suppose . Then is the autocorrelation function of a WSS r.p. if and only if there exists a satisfying such that

Thus the a.c.f. acts like a characteristic function, but also has symmetry.

If exists, then

In this case, is, in fact, a p.d.f.

More generally, is a spectral distribution of .

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_9.htm. This work is licensed under a Creative Commons License