Affiliation:
1. Delft University of Technology, Faculty of Applied Earth Sciences, P.O. Box 5028, 2600 GA Delft, The Netherlands. Emails:
Abstract
The nonuniform discrete Fourier transform (NDFT) can be computed with a fast algorithm, referred to as the nonuniform fast Fourier transform (NFFT). In L dimensions, the NFFT requires [Formula: see text] operations, where M𝓁 is the number of Fourier components along dimension 𝓁, N is the number of irregularly spaced samples, and ε is the required accuracy. This is a dramatic improvement over the [Formula: see text] operations required for the direct evaluation (NDFT). The performance of the NFFT depends on the lowpass filter used in the algorithm. A truncated Gauss pulse, proposed in the literature, is optimized. A newly proposed filter, a Gauss pulse tapered with a Hanning window, performs better than the truncated Gauss pulse and the B-spline, also proposed in the literature. For small filter length, a numerically optimized filter shows the best results. Numerical experiments for 1-D and 2-D implementations confirm the theoretically predicted accuracy and efficiency properties of the algorithm.
Publisher
Society of Exploration Geophysicists
Subject
Geochemistry and Petrology,Geophysics
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