Geodesic
On discrete Fourier spectrum of a harmonic with random frequency modulation
Waldemar Popiński1
1 Space Research Centre Polish Academy of Sciences Bartycka 18a 00-716 Warszawa, Poland
Applicationes Mathematicae, Tome 40 (2013) no. 1, pp. 99-108

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/am40-1-6
Keywords: asymptotic properties discrete fourier transform spectrum complex monochromatic oscillation frequency randomly distorted observation times ldots n series independent identically distributed fluctuations investigated proved second moments spectrum discrete fourier frequencies converge uniformly zero infty certain frequency fluctuation distributions observed effect occurs even frequency fluctuations magnitude arbitrarily small comparison original oscillation frequency

Waldemar Popiński 1

1 Space Research Centre Polish Academy of Sciences Bartycka 18a 00-716 Warszawa, Poland 
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Waldemar Popiński. On discrete Fourier spectrum of a harmonic with random frequency modulation. Applicationes Mathematicae, Tome 40 (2013) no. 1, pp. 99-108. doi: 10.4064/am40-1-6

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