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I am trying to develop a radar simulation system that is able to generate random processes whose elements are taken from a specified probability density function and have also have a specified correlation or power spectral density (psd).

I can generate i.i.d. processes from pretty much any pdf, and I can generate any power spectrum you like, however, in this case one plus one does not make two because after correlating, the pdf of the data changes.

I have read Sondhi's ,,Random Processes with Specified Spectral Denisty and First Order Probability Density Functions'' Bell Labs 1983, but am wondering what other methods exist.

So, I ask of you, what are some methods I can use to generate a random process with a specified pdf and correlation/psd?

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  • $\begingroup$ Unless you are dealing with Gaussian processes, what you are asking is very difficult, in general, if only because a random process characterization is much more complicated than a "pdf". $\endgroup$ – Stelios Feb 13 at 16:48
  • $\begingroup$ @Stelios Indeed, I know. Do you know of any review articles or books on this subject I could take a look at? I just need to get my feet on solid ground so to speak so I can start figuring out the real question. $\endgroup$ – The Dude Feb 13 at 18:26
  • $\begingroup$ I am afraid I don't know of any relevant reference. Maybe mention explicitly in your question what random process you want to generate, the context, etc. I doubt anyone can provide you any guidance for the general case. $\endgroup$ – Stelios Feb 13 at 21:27

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