Asymptotic properties of the Discrete Fourier Transform spectrum of a complex monochromatic oscillation with frequency randomly distorted at the observation times t=0,1,..., 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 → ∞ for certain frequency fluctuation distributions. The observed effect occurs even for frequency fluctuations with magnitude arbitrarily small in comparison to the original oscillation frequency.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am40-1-6,
author = {Waldemar Popi\'nski},
title = {On discrete Fourier spectrum of a harmonic with random frequency modulation},
journal = {Applicationes Mathematicae},
volume = {40},
year = {2013},
pages = {99-108},
zbl = {1273.62232},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-1-6}
}
Waldemar Popiński. On discrete Fourier spectrum of a harmonic with random frequency modulation. Applicationes Mathematicae, Tome 40 (2013) pp. 99-108. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-1-6/