On discrete Fourier spectrum of a harmonic with random frequency modulation

Volume 40 / 2013

Waldemar Popiński Applicationes Mathematicae 40 (2013), 99-108 MSC: 62M15, 62F12. DOI: 10.4064/am40-1-6

Abstract

Asymptotic properties of the Discrete Fourier Transform spectrum of a complex monochromatic oscillation with frequency randomly distorted at the observation times $t=0,1,\ldots ,n-1$ by a series of independent and identically distributed fluctuations is investigated. It is proved that the second moments of the spectrum at the discrete Fourier frequencies converge uniformly to zero as $n\to \infty $ for certain frequency fluctuation distributions. The observed effect occurs even for frequency fluctuations with magnitude arbitrarily small in comparison to the original oscillation frequency.

Authors

  • Waldemar PopińskiSpace Research Centre
    Polish Academy of Sciences
    Bartycka 18a
    00-716 Warszawa, Poland
    e-mail

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