On the second derivative of a Gaussian process envelope

Ali Abdi, IEEE

Document Type

Article

Publication Date

5-1-2002

Abstract

In this correspondence, we explore some dynamic characteristics of the envelope of a bandpass Gaussian process, which are of interest in wireless fading channels. Specifically, we show that unlike the first derivative, the second derivative of the envelope, which appears in a number of applications, does not exist in the traditional mean square sense. However, we prove that the envelope is twice differentiable almost everywhere (with probability one) if the power spectrum of the bandpass Gaussian process satisfies a certain condition. We also derive an integral form for the probability density function (pdf) of the second derivative of the envelope, assuming an arbitrary power spectrum.

Identifier

0036566761 (Scopus)

Publication Title

IEEE Transactions on Information Theory

External Full Text Location

https://doi.org/10.1109/18.995654

ISSN

00189448

First Page

1226

Last Page

1231

Issue

5

Volume

48

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