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A note on Gaussian processes and zero-memory non-linear transformations

Published online by Cambridge University Press:  14 July 2016

Elias Masry
Elias Masry*
Affiliation:
University of California at San Diego
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Abstract

We consider the problem of the distinguishability between Gaussian processes observed through non-linear systems. For a broad class 𝒜 of zero-memory time-dependent non-linear transformations, the following uniqueness relationship is obtained. If Xi, i = 1, 2 are two normalized jointly Gaussian processes, then they are indistinguishable if and only if their transformed processes Yi = A[Xi], i = 1, 2, A ∈ 𝒜, are indistinguishable. Some interesting examples of functions in 𝒜 are presented.

Keywords

GAUSSIAN PROCESSESNON-LINEAR TRANSFORMATIONSINDISTINGUISHABLE PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 4 , December 1977 , pp. 857 - 861
Copyright
Copyright © Applied Probability Trust 1977 

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Footnotes

This work was supported by the Office of Naval Reasearch under Contract N00014–75-C-0652.

References

[1] Barrett, J. F. and Lampard, D. G. (1955) An expansion of some second-order probability distributions and its application to noise problems. IEEE Trans. Inf. Theory 1, 10–15.Google Scholar
[2] Masry, E. and Cambanis, S. (1976) Bandlimited processes and certain nonlinear transformations. J. Math. Anal. Appl. 53, 59–77.Google Scholar