Can a Fourier transform be performed on irregularly sampled data with timestamps?

Question

Normally, when I think of performing a Fourier transform, I imagine that my samples are spaced regularly in time (or space).

If I have a set of samples that are spaced irregularly, but have accurate timestamps, is it still possible to perform a Fourier transform?

I would guess this is what trigonometric interpolation is all about, but I am no specialist. One thing I am sure is that FFT (the fast Fourier transform algorithm) does not apply here. — Mateusz Kwaśnicki, Commented Jan 29, 2021 at 10:08

Bastian Seifert · Accepted Answer · 2021-01-29 13:02:11Z

4

How to do this in a fast way is explained in Plonka et al., "Fast Fourier Transforms for Nonequispaced Data", in Numerical Fourier Analysis pp 377-419, https://link.springer.com/chapter/10.1007/978-3-030-04306-3_7

answered Jan 29, 2021 at 13:02

Bastian Seifert

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$\begingroup$ Huh! Now there is not even a single thing I am sure. Interesting! $\endgroup$
– Mateusz Kwaśnicki
Commented Jan 29, 2021 at 13:44
1

$\begingroup$ @MISC {382541, TITLE = {Can a Fourier transform be performed on irregularly sampled data with timestamps?}, AUTHOR = {seopaslaugos (mathoverflow.net/users/101157/bastian-seifert)}, HOWPUBLISHED = {MathOverflow}, NOTE = {URL:mathoverflow.net/q/382541 (version: 2021-01-29)}, EPRINT = {mathoverflow.net/q/382541}, URL = {mathoverflow.net/q/382541} } Very interesting, thanks for sharing! $\endgroup$
– Donatas Pocius
Commented Jan 29, 2021 at 14:41

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