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Open AccessArticle

Calculation of Entropy for a Sinusoid with Beta-Distributed Phase

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U.S. Naval Research Laboratory, Optical Science Division, Washington DC 20375, USA
2
NRC Postdoctoral Research Associate, Naval Research Laboratory, Optical Science Division, Washington DC 20375, USA
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Author to whom correspondence should be addressed.
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Permanent Address: Global Strategies Group, Crofton, MD 21114, USA.
Entropy 2009, 11(4), 949-958; https://doi.org/10.3390/e11040949
Received: 17 September 2009 / Accepted: 13 November 2009 / Published: 2 December 2009
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. View Full-Text
Keywords: differential entropy; sine wave; Beta distribution; phase noise differential entropy; sine wave; Beta distribution; phase noise
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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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