dorsal/arxiv
View SchemaSigSpec - I. Frequency- and Phase-Resolved Significance in Fourier Space
| Authors | P. Reegen |
|---|---|
| Categories | |
| ArXiv ID | physics/0703160 |
| URL | https://arxiv.org/abs/physics/0703160 |
| DOI | 10.1051/0004-6361:20066597 |
Abstract
Identifying frequencies with low signal-to-noise ratios in time series of stellar photometry and spectroscopy, and measuring their amplitude ratios and peak widths accurately, are critical goals for asteroseismology. These are also challenges for time series with gaps or whose data are not sampled at a constant rate, even with modern Discrete Fourier Transform (DFT) software. Also the False-Alarm Probability introduced by Lomb and Scargle is an approximation which becomes less reliable in time series with longer data gaps. A rigorous statistical treatment of how to determine the significance of a peak in a DFT, called SigSpec, is presented here. SigSpec is based on an analytical solution of the probability that a DFT peak of a given amplitude does not arise from white noise in a non-equally spaced data set. The underlying Probability Density Function (PDF) of the amplitude spectrum generated by white noise can be derived explicitly if both frequency and phase are incorporated into the solution. In this paper, I define and evaluate an unbiased statistical estimator, the "spectral significance", which depends on frequency, amplitude, and phase in the DFT, and which takes into account the time-domain sampling. I also compare this estimator to results from other well established techniques and demonstrate the effectiveness of SigSpec with a few examples of ground- and space-based photometric data, illustratring how SigSpec deals with the effects of noise and time-domain sampling in determining significant frequencies.
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"abstract": "Identifying frequencies with low signal-to-noise ratios in time series of\nstellar photometry and spectroscopy, and measuring their amplitude ratios and\npeak widths accurately, are critical goals for asteroseismology. These are also\nchallenges for time series with gaps or whose data are not sampled at a\nconstant rate, even with modern Discrete Fourier Transform (DFT) software. Also\nthe False-Alarm Probability introduced by Lomb and Scargle is an approximation\nwhich becomes less reliable in time series with longer data gaps. A rigorous\nstatistical treatment of how to determine the significance of a peak in a DFT,\ncalled SigSpec, is presented here. SigSpec is based on an analytical solution\nof the probability that a DFT peak of a given amplitude does not arise from\nwhite noise in a non-equally spaced data set. The underlying Probability\nDensity Function (PDF) of the amplitude spectrum generated by white noise can\nbe derived explicitly if both frequency and phase are incorporated into the\nsolution. In this paper, I define and evaluate an unbiased statistical\nestimator, the \"spectral significance\", which depends on frequency, amplitude,\nand phase in the DFT, and which takes into account the time-domain sampling. I\nalso compare this estimator to results from other well established techniques\nand demonstrate the effectiveness of SigSpec with a few examples of ground- and\nspace-based photometric data, illustratring how SigSpec deals with the effects\nof noise and time-domain sampling in determining significant frequencies.",
"arxiv_id": "physics/0703160",
"authors": [
"P. Reegen"
],
"categories": [
"physics.data-an",
"astro-ph.IM",
"stat.ME"
],
"doi": "10.1051/0004-6361:20066597",
"title": "SigSpec - I. Frequency- and Phase-Resolved Significance in Fourier Space",
"url": "https://arxiv.org/abs/physics/0703160"
},
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