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Bessel representation for amplitude distribution of noisy sinusoidal signals


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.

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The author is grateful to the anonymous Reviewer for careful reading of the original manuscript and for pointing out relevant references as well as for insightful remarks. This research was supported by the Russian state budget funding in 2018–2020.

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Correspondence to Mikhail Trifonov.

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Trifonov, M. Bessel representation for amplitude distribution of noisy sinusoidal signals. Stat Papers (2021).

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  • Probability density functions
  • Gaussian noise
  • Sinusoidal signal
  • Bessel functions

Mathematics Subject Classification

  • 60E05
  • 62E15
  • 62M10
  • 33C10
  • 33C45