Estimating the bandwidth of a normal process from the level crossings of its envelope

Komaili, J.; Ferrari, Leonard A.; Sankar, P. V.

doi:10.1109/tassp.1987.1165038

Cited by 6 publications

(1 citation statement)

References 2 publications

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“…The envelope of a bandpass Gaussian process is a slowly varying process that conveys useful information about the Gaussian process. For an arbitrary power spectrum, the envelope has a Rayleigh probability density function (PDF) [1], while it has been shown by several authors, independently, that its first derivative has a Gaussian PDF [2] [3] [4] [5] [6]. However, only the conditional PDF of the envelope second derivative has been studied so far, assuming an even-symmetric power spectrum [7].…”

Section: Introductionmentioning

confidence: 99%

On the second derivative of a Gaussian process envelope

Abdi

2002

IEEE Trans. Inform. Theory

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In this paper 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 of the second derivative of the envelope, assuming an arbitrary power spectrum.

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