Fourier transforms of data sampled in unequally spaced segments.
Abstract
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. Hilbertspace 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 piecewisesampled 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.
 Publication:

The Astronomical Journal
 Pub Date:
 January 1979
 DOI:
 10.1086/112397
 Bibcode:
 1979AJ.....84..116M
 Keywords:

 Astronomical Spectroscopy;
 Data Sampling;
 Fourier Transformation;
 Heuristic Methods;
 Hilbert Space;
 Time Series Analysis;
 Astronomy;
 Mathematics;
 Computing;
 Data Processing