Fourier analysis with unequally-spaced data

Deeming, Terence J.

doi:10.1007/bf00681947

Cited by 659 publications

(434 citation statements)

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“…The most commonly used tool for periodicity analysis of both evenly and unevenly sampled signals is the so-called Periodogram (hereafter P), which is an estimator of the signal energy in the frequency domain (Deeming 1975), and has been extensively applied to the study of light curves of variable stars, both periodic and semi-periodic. In the case of even sampling, the Periodogram has a simple statistical distribution (exponentially distributed for Gaussian noise).…”

Section: The Periodogram (P) Methodsmentioning

confidence: 99%

A multifrequency analysis of radio variability of blazars

Ciaramella

Bongardo

Aller

et al. 2004

A&A

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Abstract.We have carried out a multifrequency analysis of the radio variability of blazars, exploiting the data obtained during the extensive monitoring programs carried out at the University of Michigan Radio Astronomy Observatory (UMRAO, at 4.8, 8, and 14.5 GHz) and at the Metsähovi Radio Observatory (22 and 37 GHz). Two different techniques detect, in the Metsähovi light curves, evidence of periodicity at both frequencies for 5 sources (0224 + 671, 0945 + 408, 1226 + 023, 2200 + 420, and 2251 + 158). For the last three sources, consistent periods are found also at the three UMRAO frequencies and the Scargle (1982) method yields an extremely low false-alarm probability. On the other hand, the 22 and 37 GHz periodicities of 0224+671 and 0945 + 408 (which were less extensively monitored at Metsähovi and for which we get a significant false-alarm probability) are not confirmed by the UMRAO database, where some indications of ill-defined periods of about a factor of two longer are retrieved. We have also investigated the variability index, the structure function, and the distribution of intensity variations of the most extensively monitored sources. We find a statistically significant difference in the distribution of the variability index for BL Lac objects compared to flat-spectrum radio quasars (FSRQs), in the sense that the former objects are more variable. For both populations the variability index steadily increases with increasing frequency. The distribution of intensity variations also broadens with increasing frequency, and approaches a log-normal shape at the highest frequencies. We find that variability enhances by 20-30% the high frequency counts of extragalactic radio-sources at bright flux densities, such as those of the WMAP and P surveys. In all objects with detected periodicity we find evidence for the existence of impulsive signals superimposed on the periodic component.

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Section: The Periodogram (P) Methodsmentioning

confidence: 99%

A multifrequency analysis of radio variability of blazars

Ciaramella

Bongardo

Aller

et al. 2004

A&A

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“…For the frequency analysis, we employed the code pasper (Diago et al 2008), which is based on the classical discrete Fourier transform (Deeming 1975;Scargle 1982) and the least-square fitting of a sinusoidal function in the time domain. When a frequency is found, it is prewhitened from the original data and a new step starts looking for a new frequency in the residuals.…”

Section: Frequency Analysismentioning

confidence: 99%

Pulsations in the late-type Be star HD 50 209 detected by CoRoT

Diago¹,

Gutiérrez‐Soto

Auvergne

et al. 2009

A&A

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Context. The presence of pulsations in late-type Be stars is still a matter of controversy. It constitutes an important issue to establish the relationship between non-radial pulsations and the mass-loss mechanism in Be stars. Aims. To contribute to this discussion, we analyse the photometric time series of the B8IVe star HD 50 209 observed by the CoRoT mission in the seismology field. Methods. We use standard Fourier techniques and linear and non-linear least squares fitting methods to analyse the CoRoT light curve. In addition, we applied detailed modelling of high-resolution spectra to obtain the fundamental physical parameters of the star. Results. We have found four frequencies which correspond to gravity modes with azimuthal order m = 0, −1, −2, −3 with the same pulsational frequency in the co-rotating frame. We also found a rotational period with a frequency of 0.679 cd −1 (7.754 μHz). Conclusions. HD 50 209 is a pulsating Be star as expected from its position in the HR diagram, close to the SPB instability strip.

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“…In the astronomy literature, this is referred to as the Deeming periodogram; its properties in estimating frequency are discussed in Deeming (1975). A version of the periodogram which is equivalent to least squares with a single cosinusoid was introduced by Lomb (1976) and Scargle (1982), and is referred to as the Lomb-Scargle periodogram.…”

Section: Numerical Examplesmentioning

confidence: 99%

Nonparametric estimation of a periodic function

Hall¹,

Reimann²,

Rice³

2000

Biometrika

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ABSTRACT. Motivated by applications to brightness data on periodic variable stars, we study nonparametric methods for estimating both the period and the amplitude function from noisy observations of a periodic function made at irregularly spaced times. It is shown that nonparametric estimators of period converge at parametric rates and attain a semiparametric lower bound which is the same if the shape of the periodic function is unknown as if it were known. Also, first-order properties of nonparametric estimators of the amplitude function are identical to those that would obtain if the period were known. Numerical simulations and applications to real data show the method to work well in practice.KEY WORDS AND PHRASES. frequency estimation, nonparametric regression, semiparametric estimation, Nadaraya-Watson estimator, MACHO project, variable star data.

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Fourier analysis with unequally-spaced data

Cited by 659 publications

References 1 publication

A multifrequency analysis of radio variability of blazars

A multifrequency analysis of radio variability of blazars

Pulsations in the late-type Be star HD 50 209 detected by CoRoT

Nonparametric estimation of a periodic function

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