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Entropy 2009, 11(4), 949-958; doi:10.3390/e11040949
Article

Calculation of Entropy for a Sinusoid with Beta-Distributed Phase

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Received: 17 September 2009 / Accepted: 13 November 2009 / Published: 2 December 2009
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Abstract

In this paper, an analytical expression is developed for the differential entropy of a sinusoid with a Beta-distributed phase angle. This particular signal model is prevalent in optical communications, however an expression for the associated differential entropy does not currently exist. The expression we derive is approximate as it relies on a series expansion for one of the key terms needed in the derivation. However, we are able to show that the approximation is accurate (error ≤ 5%) for a wide variety of Beta parameter choices.
Keywords: differential entropy; sine wave; Beta distribution; phase noise differential entropy; sine wave; Beta distribution; phase noise
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Michalowicz, J.V.; Olson, C.C.; Bucholtz, F.; Nichols, J.M. Calculation of Entropy for a Sinusoid with Beta-Distributed Phase. Entropy 2009, 11, 949-958.

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