Representation and Generation of Non-Gaussian Wide-Sense Stationary Random Processes With Arbitrary PSDs and a Class of PDFs | IEEE Journals & Magazine | IEEE Xplore

Representation and Generation of Non-Gaussian Wide-Sense Stationary Random Processes With Arbitrary PSDs and a Class of PDFs


Abstract:

A new method for representing and generating realizations of a wide-sense stationary non-Gaussian random process is described. The representation allows one to independen...Show More

Abstract:

A new method for representing and generating realizations of a wide-sense stationary non-Gaussian random process is described. The representation allows one to independently specify the power spectral density and the first-order probability density function of the random process. The only proviso is that the probability density function must be symmetric and infinitely divisible. The method proposed models the sinusoidal component frequencies as random variables, a key departure from the usual representation a of wide-sense stationary random process by the spectral theorem. Ergodicity in the mean and autocorrelation is also proven, under certain conditions. An example is given to illustrate its application to the K distribution, which is important in many physical modeling problems in radar and sonar.
Published in: IEEE Transactions on Signal Processing ( Volume: 58, Issue: 7, July 2010)
Page(s): 3448 - 3458
Date of Publication: 22 March 2010

ISSN Information:


I. Introduction

We consider the problem of how to generate realizations from a random process that is wide-sense stationary with a given continuous power spectral density (PSD) and with a given first-order marginal probability density function (PDF). This is a problem that has important practical implications. The usual approach is to use a linear time invariant filter to filter white noise, yielding the desired PSD, and then a nonlinearity to convert the PDF to the desired one, if possible. The difficulty with this approach is that the PSD and the PDF are linked together, changing one requires a change of the other. Some of the many approaches using this technique can be found in [1], [2], [13], [14] and the references contained therein. We next summarize some of the difficulties in applying these approaches. In the scheme proposed in [1], a white Gaussian random process is filtered and then followed by a nonlinearity. The autocorrelation sequence at the output of the filter may not be positive definite and hence the method can fail. Ergodicity is not addressed. In addition, the method is fairly complex to implement. When it can be implemented, however, there are no restrictions on the PDF. In [2], a correlated Gaussian random process is multiplied by a modulating sequence. The main problem is in determining the modulating sequence, which can be difficult if not impossible. Furthermore, the generated sequence is not ergodic. An approach given in [14] is based on [1] and is claimed to alleviate some of the drawbacks. However, it can only produce wide-sense stationary and ergodic sequences asymptotically or as the data record length goes to infinity. Finally, in [13], a nonlinear autoregression is used. It does not appear that an arbitrary PSD may be specified. Finally, due to the nonlinearities employed in the above schemes it is doubtful if the results can be extended to the more general cases of multidimensional and multichannel random processes. The latter will impose even more restrictions between the PSD and the PDF.

References

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