my problem is the following: I have N different measurements of a quantity which depends on two other quantities that I also know. I would like to use find a function two variable function that approximates the data, and I thought that using Fourier transforms was a nice idea. Does anybody has a suggestion on how should I proceed? I think as a first step I want to do a FFT of my data, but then how can I implement the inverse FT not only for the points where I measured but for any pair (x,y) as input? Thanks a lot. (I am using python).
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here on SO questions should be programming focused with a short reproducible code example ... this is not an advise column ... please read the freq asked questions ... How to create a Minimal, Complete, and Verifiable example https://stackoverflow.com/help/mcve ... there is a data science counterpart forum https://datascience.stackexchange.com which may be a better fit – Scott Stensland Nov 14 '19 at 21:13
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I think this question is most suitable for dsp.stackexchange.com. – Robert Dodier Nov 15 '19 at 00:29
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This is more of a math question. Unless your function is periodic, I don't see how a Fourier transform helps you with fitting a function per se. Also note that the FFT requires equal point spacing. As for the Inverse transform (spectrum back to time or xy) you can calculate the Fourier integral directly for other points. But those points are not much more than a sinc-window (so no new information, the FFT preserves the information content). Add a graph. Or see : https://stackoverflow.com/questions/21566379/fitting-a-2d-gaussian-function-using-scipy-optimize-curve-fit-valueerror-and-m) – roadrunner66 Nov 15 '19 at 01:39