On discrete Fourier spectrum of a harmonic with random frequency modulation
Applicationes Mathematicae, Tome 40 (2013) no. 1, p. 99-108.
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.
Source:
Zbl
Classification : 62F12, 62M15, 42A38 
@article{APME_2013__40_1_280074,
     author = {Waldemar Popi\'nski},
     title = {On discrete {Fourier} spectrum of a harmonic with random frequency modulation},
     journal = {Applicationes Mathematicae},
     pages = {99-108},
     volume = {40},
     number = {1},
     year = {2013},
     zbl = {an:1273.62232},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/APME_2013__40_1_280074/}
}
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Waldemar Popiński. On discrete Fourier spectrum of a harmonic with random frequency modulation. Applicationes Mathematicae, Tome 40 (2013) no. 1, p. 99-108. https://geodesic-test.mathdoc.fr/item/APME_2013__40_1_280074/