On discrete Fourier spectrum of a harmonic with random frequency modulation

@article{WaldemarPopiński2013,
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,..., 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.},
author = {Waldemar Popiński},
journal = {Applicationes Mathematicae},
keywords = {discrete Fourier transform; monochromatic harmonic; spectrum estimation; random frequency modulation},
language = {eng},
number = {1},
pages = {99-108},
title = {On discrete Fourier spectrum of a harmonic with random frequency modulation},
url = {http://eudml.org/doc/280074},
volume = {40},
year = {2013},
}

TY - JOUR
AU - Waldemar Popiński
TI - On discrete Fourier spectrum of a harmonic with random frequency modulation
JO - Applicationes Mathematicae
PY - 2013
VL - 40
IS - 1
SP - 99
EP - 108
AB - 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.
LA - eng
KW - discrete Fourier transform; monochromatic harmonic; spectrum estimation; random frequency modulation
UR - http://eudml.org/doc/280074
ER -