Least - squares frequency analysis of unequally spaced data
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Cites methods from "Least - squares frequency analysis ..."
...(2004), using a method based on the Lomb-Scargle periodogram (Lomb, 1976)....
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...To compute the frequency content of uncensored data, we applied a least squares spectral analysis adapted for nonuniformly sampled data, as described in Mathias et al. (2004), using a method based on the Lomb-Scargle periodogram (Lomb, 1976)....
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1,777 citations
Cites methods from "Least - squares frequency analysis ..."
...A Lomb periodogram [15] was used to calculate the power spectrum [33], [34] of the heart rate time series because it can directly use unevenly sampled interbeat interval data and because it is robust to missed beats [35]....
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...The EKG electrodes were placed in a modified lead II configuration to minimize motion artifacts and to maximize the amplitude of the R-waves, since both the heart rate [13] and heart rate variability (HRV) [14], [15] algorithms used in this analysis depend on R-wave peak detection....
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1,367 citations
Cites background or methods from "Least - squares frequency analysis ..."
...Lomb (1976) showed that if data are Gaussian noise, the termsŶC 2 /ĈC and ŶS 2 /Ŝ S in Eq....
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...The analytic solution for the generalised Lomb-Scargle periodogram can be obtained in a straightforward manner in the same way as outlined in Lomb (1976)....
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...The equation for the periodogram was given by Barning (1963), and also Lomb (1976) and Scargle (1982), who furthermore investigated its statistical behaviour, especially the statistical significance of the detection ofa signal....
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...As already mentioned by Lomb (1976) Eq....
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...For a time series (ti , yi) with zero mean (y = 0), the LombScargle periodogram is defined as (normalisation from Lomb 1976): p̂(ω) = 1 ŶY ŶC 2 τ̂ ĈCτ̂ + ŶS 2 τ̂ Ŝ Ŝτ (1) = 1 ∑ i y 2 i [∑ i yi cosω(ti − τ̂) ]2 ∑ i cos2ω(ti − τ̂) + [∑ i yi sinω(ti − τ̂) ]2 ∑ i sin 2ω(ti − τ̂) …...
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1,142 citations
Cites methods from "Least - squares frequency analysis ..."
...For the integrated analysis, per omics set, for each time-series curve the Lomb-Scargle transformation (Hocke and Kämpfer, 2009; Lomb, 1976; Scargle, 1982, 1989) for unevenly sampled gapped time-series data was implemented (Ahdesmaki et al....
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...For the integrated analysis, per omics set, for each time-series curve the Lomb-Scargle transformation (Hocke and Kämpfer, 2009; Lomb, 1976; Scargle, 1982, 1989) for unevenly sampled gapped time-series data was implemented (Ahdesmäki et al., 2007; Glynn et al., 2006; Van Dongen et al., 1999; Yang…...
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References
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"Least - squares frequency analysis ..." refers background in this paper
...For simplicity let us put is the bivariate normal probability function for variables x and y, with zero mean, unit variance and correlation e. Equation 26.3.2 of the Handbook of Mathematical Functions (Abramowitz and Stegun, 1964) gives where Z(x) is the normal probability function for a variable with zero mean and unit variance....
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...…bivariate normal probability function for variables x and y, with zero mean, unit variance and correlation e. Equation 26.3.2 of the Handbook of Mathematical Functions (Abramowitz and Stegun, 1964) gives where Z(x) is the normal probability function for a variable with zero mean and unit variance....
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2,362 citations
298 citations
40 citations
"Least - squares frequency analysis ..." refers methods in this paper
...A slightly modified form of periodogram analysis has been devised by Gray and Desikachary (1973), in which prewhitening is carried out in the frequency domain instead of the time domain....
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24 citations
"Least - squares frequency analysis ..." refers methods in this paper
...A model of the observed short period variation in the ~ Vir 1934 velocities (Shobbrook et al., 1972) was set up....
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