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Kunis, S. ; Melzer, I.*

A stable and accurate butterfly sparse fourier transform.

SIAM J. Numer. Anal. 50, 1777-1800 (2012)
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Recently, the butterfly approximation scheme was proposed for computing Fourier transforms with sparse and smooth sampling in the frequency and spatial domains. We present a rigorous error analysis which shows how the local expansion degree depends on the target accuracy and the nonharmonic bandwidth. Moreover, we show that the original scheme becomes numerically unstable if a large local expansion degree is used. This problem is removed by representing all approximations in a Lagrange-type basis instead of the previously used monomial basis. All theoretical results are illustrated by numerical experiments.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Trigonometric Approximation ; Nonharmonic Fourier Series ; Fast Fourier Transform; Algorithm
ISSN (print) / ISBN 0036-1429
e-ISSN 1095-7170
Quellenangaben Band: 50, Heft: 3, Seiten: 1777-1800 Artikelnummer: , Supplement: ,
Verlag Society for Industrial and Applied Mathematics (SIAM)