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

Calculation of Entropy for a Sinusoid with Beta-Distributed Phase

1,#email, 2,* email, 1email and 1email
Received: 17 September 2009; Accepted: 13 November 2009 / Published: 2 December 2009
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.
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
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MDPI and ACS Style

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.

AMA Style

Michalowicz JV, Olson CC, Bucholtz F, Nichols JM. Calculation of Entropy for a Sinusoid with Beta-Distributed Phase. Entropy. 2009; 11(4):949-958.

Chicago/Turabian Style

Michalowicz, Joseph V.; Olson, Colin C.; Bucholtz, Frank; Nichols, Jonathan M. 2009. "Calculation of Entropy for a Sinusoid with Beta-Distributed Phase." Entropy 11, no. 4: 949-958.

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