Fourier Techniques for Very Long Astrophysical Time-Series Analysis

By S. Ransom, S. Eikenberry, J. Middleditch. 2002

356 citations recorded by the source corpus.

We present an assortment of both standard and advanced Fourier techniques that are useful in the analysis of astrophysical time series of very long duration—where the observation time is much greater than the time resolution of the individual data points. We begin by reviewing the operational characteristics of Fourier transforms of time-series data, including power-spectral statistics, discussing some of the differences between analyses of binned data, sampled data, and event data, and we briefly discuss algorithms for calculating discrete Fourier transforms (DFTs) of very long time series. We then discuss the response of DFTs to periodic signals and present techniques to recover Fourier amplitude "lost" during simple traditional analyses if the periodicities change frequency during the observation. These techniques include Fourier interpolation, which allows us to correct the response for signals that occur between Fourier frequency bins. We then present techniques for estimating additional signal properties such as the signal's centroid and duration in time, the first and second derivatives of the frequency, the pulsed fraction, and an overall estimate of the significance of a detection. Finally, we present a recipe for a basic but thorough Fourier analysis of a time series for well-behaved pulsations.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/398da84c5bc49013dc46c0cd94bb52c6f67e36ad

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Citations in the corpus

A CATALOG OF X-RAY POINT SOURCES FROM TWO MEGASECONDS OF CHANDRA OBSERVATIONS OF THE GALACTIC CENTER (2008, background): “Here, Pmeas is normalized to have a mean value of 1, and the approximation is valid for Pmeas 1 (Ransom et al. 2002).”
Eight New Millisecond Pulsars in NGC 6440 and NGC 6441 (2007, methodology): “…each time series using TEMPO.10 We Fourier-transformed each time series and searched them using a frequency-domain acceleration search technique (Ransom et al. 2002) that allows a fully coherent search in frequency/ frequency-derivative space, as well as the incoherent addition of a number of…”
THE SECOND FERMI LARGE AREA TELESCOPE CATALOG OF GAMMA-RAY PULSARS (2013, methodology): “A key feature of radio pulsar searches is that they are sensitive to binary systems with the application of techniques to correct for the orbital acceleration in short data sets (with durations much less than the binary period, Ransom et al. 2002).”
The Parkes Multibeam Pulsar Survey - V. Finding binary and millisecond pulsars (2004, methodology): “Alternatively, in the frequency domain, an FFT of the zero acceleration time series is performed and then a series of matched filters is applied to correct the frequency spectrum to look for accelerated periodicities (e.g. Ransom et al. 2002).”
1E 1547.0–5408: A Radio-emitting Magnetar with a Rotation Period of 2 Seconds (2007, methodology): “We analyzed the data using standard techniques implemented in PRESTO5 (Ransom et al. 2002), in similar fashion to other pulsar searches (e.g., Camilo et al. 2006a).”
An Ordinary Short Gamma-Ray Burst with Extraordinary Implications: Fermi-GBM Detection of GRB 170817A (2017, methodology): “Specifically, an accelerated search (Ransom et al. 2002) was used to search for drifting periodic signals in the range 8-1999 Hz.”
Formation of Double Neutron Star Systems (2017, background): “These include mostly “acceleration searches” (Anderson et al. 1990; Camilo et al. 2000; Ransom et al. 2002), which assume a constant acceleration during the observation.”