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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
1
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
#
Permanent Address: Global Strategies Group, Crofton, MD 21114, USA.
* Author to whom correspondence should be addressed.
Received: 17 September 2009 / Accepted: 13 November 2009 / Published: 2 December 2009
Download PDF Full-Text [256 KB, uploaded 2 December 2009 09:51 CET]
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 StyleMichalowicz 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 StyleMichalowicz, 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.