Bessel representation for amplitude distribution of noisy sinusoidal signals

Mikhail Trifonov ()
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Mikhail Trifonov: Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences

Statistical Papers, 2022, vol. 63, issue 3, No 11, 983-988

Abstract: Abstract A new representation for the probability density function (PDF) of a single real sinusoid in additive white Gaussian noise is presented. It has the form of an infinite series of the exponentially scaled modified Bessel functions of the first kind of integer order. The new PDF is an alternative to the classical PDF’s expressed in terms of the derivatives of the error function, the confluent hypergeometric function of the first kind, and the exponentially scaled Hermite polynomials.

Keywords: Probability density functions; Gaussian noise; Sinusoidal signal; Bessel functions; 60E05; 62E15; 62M10; 33C10; 33C45 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00362-021-01262-z

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