research-article

An exact solution to the Fourier Transform of band-limited periodic functions with nonequispaced data and application to non-periodic functions

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https://doi.org/10.1016/j.jcp.2022.111806

Published: 01 February 2023 Publication History

Abstract

The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or seismology. Iterative methods have been developed that allow to reach approximate solutions. Here an exact solution to the problem for band-limited periodic signals is presented. The exact spectrum can be deduced from the spectrum of the non-equispaced data through the inversion of a Toeplitz matrix. The result applies to data of any dimension. This method also provides an excellent approximation for non-periodic band-limit signals. The method allows to reach very high dynamic ranges (10¹³ with double-float precision) which depend on the regularity of the samples.

Highlights

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Fourier Transform.

•

Irregular sampling.

•

Nonequispaced data.

•

Band-limited functions.

•

Toeplitz matrices.

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An exact solution to the Fourier Transform of band-limited periodic functions with nonequispaced data and application to non-periodic functions

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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 474, Issue C

Feb 2023

1279 pages

ISSN:0021-9991

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Elsevier Inc.

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Academic Press Professional, Inc.

United States

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Published: 01 February 2023

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Abstract

Highlights

References

Index Terms

Recommendations

Numerical stability of nonequispaced fast Fourier transforms

Periodic functions and the discrete Fourier transform: a time-domain view

The discrete periodic Radon transform

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