Fourier transforms of data sampled in unequally spaced segments

Details Fourier transforms of data sampled in unequally spaced segments Fourier transforms of data sampled in unequally spaced segments

Jan 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979aj.....84..116m&link_type=abstract

Astronomical Journal, vol. 84, Jan. 1979, p. 116-126.

Astronomy and Astrophysics

Astronomy

10

Astronomical Spectroscopy, Data Sampling, Fourier Transformation, Heuristic Methods, Hilbert Space, Time Series Analysis

Scientific paper

A general procedure for processing segmented data sets is given which is most efficient for data sets where large gaps occur between data 'clumps' and when the data subsets are made up of equal or nearly equal interval (within 20%) point distributions. Hilbert-space formulations are followed, a method for obtaining the compound Fourier transform of a continuous function sampled in finite segments of arbitrary spacing is outlined, and the pathology of piecewise-sampled functions is ivestigated. The morphology of Fourier transforms is considered in certain idealized and schematic cases, and a technique is derived for stacking individual Fourier transforms in correct phase. The various factors that influence the reliability of Fourier transforms and discrete Fourier transforms are discussed.

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