Discrete Fourier Transforms of Nonuniformly Spaced Data

Details Discrete Fourier Transforms of Nonuniformly Spaced Data Discrete Fourier Transforms of Nonuniformly Spaced Data

Nov 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982aj.....87.1608s&link_type=abstract

ASTRONOMICAL JOURNAL V. 87, P.1608, 1982

Astronomy and Astrophysics

Astronomy

10

Scientific paper

Time series or spatial series of measurements taken with nonuniform spacings have failed to yield fully to analysis using the Discrete Fourier Transform (DFT). This is due to the fact that the formal DFT is the convolution of the transform of the signal with the transform of the nonuniform spacings. Two original methods are presented for deconvolving such transforms for signals containing significant noise. The first method solves a set of linear equations relating the observed data to values defined at uniform grid points, and then obtains the desired trans- form as the DFT of the uniform interpolates. The second method solves a set of linear equations relating the real and imaginary components of the formal DFT directly to those of the desired transform. The results of numerical experiments with noisy data are presented in order to demonstrate the capabilities and limitations of the methods.

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