On discrete Fourier spectrum of a harmonic with random frequency modulation
Volume 40 / 2013
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.
