The analysis of indexed astronomical time series – XII. The statistics of oversampled Fourier spectra of noise plus a single sinusoid

dc.contributor.authorKoen, Chris
dc.date.accessioned2015-12-14T09:41:01Z
dc.date.available2015-12-14T09:41:01Z
dc.date.issued2015
dc.description.abstractWith few exceptions, theoretical studies of periodogram properties focus on pure noise time series. This paper considers the case in which the time series consists of noise together with a single sinusoid, observed at regularly spaced time points. The distribution of the periodogram ordinates in this case is shown to be of exponentially modified Gaussian form. Simulations are used to demonstrate that if the periodogram is substantially oversampled (i.e. calculated in a dense grid of frequencies), then the distribution of the periodogram maxima can be accurately approximated by a simple form (at least at moderate signal-to-noise ratios). This result can be used to derive a calculation formula for the probability of correct signal frequency identification at given values of the time series length and (true) signal-to-noise ratio. A set of curves is presented which can be used to apply the theory to, for example, asteroseismic data. An illustrative application to Kepler data is given.en_US
dc.description.accreditationWeb of Scienceen_US
dc.identifier.citationKoen, C. (2015). The analysis of indexed astronomical time series – XII. The statistics of oversampled Fourier spectra of noise plus a single sinusoid. Monthly Notices of the Royal Astronomical Society, 453(2): 1793-1798.en_US
dc.identifier.issn0035-8711
dc.identifier.urihttp://hdl.handle.net/10566/2023
dc.language.isoenen_US
dc.privacy.showsubmitterfalse
dc.publisherOxford University Pressen_US
dc.source.urihttp://dx.doi.org/10.1093/mnras/stv1744
dc.status.ispeerreviewedtrue
dc.subjectAstronomyen_US
dc.subjectPeriodogramen_US
dc.subjectAsteroseismic dataen_US
dc.subjectKepleren_US
dc.subjectSinusoidal signalen_US
dc.titleThe analysis of indexed astronomical time series – XII. The statistics of oversampled Fourier spectra of noise plus a single sinusoiden_US
dc.typeArticleen_US

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