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Can FFTW perform the FFT on data which is not uniform in time? I can't seem to find a straight-forward answer to this question anywhere online.

Royi
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John
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  • Given my (limited) knowledge of how FFT works my instinct is no. I think the standard approach to this would be to resample so you are uniform in time. Although I'm not really an expert in FFTs so I may be wrong. – nivag May 29 '14 at 16:09
  • Yeah, I'm aware that FFT requires uniform sampling, but I wasn't sure if FFTW included built-in functionality to realize when data was non-uniform and then apply a NUDFT. – John May 29 '14 at 16:21

1 Answers1

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The answer is Non-uniform discrete Fourier transform

I suggest you to take a look in here: NFFT library. Tutorial for that purpose: NFFT 3.0 Tutorial.

You can also find a Python wrapper: pyNFFT.

The generalisations of the NFFT include

NNFFT - nonequispaced in time and frequency fast Fourier transform,

NFCT/NFST - nonequispaced fast (co)sine transform,

NSFFT - nonequispaced sparse fast Fourier transform,

FPT - fast polynomial transform,

NFSFT - nonequispaced fast spherical Fourier transform,

NFSOFT - nonequispaced fast Fourier transform on the rotation group

The NFFT is a C subroutine library for computing the nonequispaced discrete Fourier transform (NDFT) in one or more dimensions, of arbitrary input size, and of complex data. New: A Matlab interface is part of the NFFT3. We believe that our library, which is free software, and based on FFTW (FFTW 3.x) should become the NFFT library of choice for most applications.

jojeck
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  • Thanks. I've actually been looking into this one, but I haven't been able to get it to work properly and was hoping I could just make FFTW work instead. – John May 29 '14 at 16:19
  • I believe that FFTW has no such functionality. For me tutorial was fairly straightforward and had no problems with using NFFT back in time. Just take a look into Chapter 5. – jojeck May 29 '14 at 16:22
  • Does the library plug and play on Windows? The guides seem to target Linux OS, so when I couldn't get it to install properly I assumed that this was to blame. – John May 29 '14 at 16:23
  • Yep, It does. Just follow steps described here. – jojeck May 29 '14 at 16:25
  • And if I don't wish to use MATLAB but rather MSVC or some other c++ editor? – John May 29 '14 at 16:26
  • MATLAB is compatibility is optional. I advise you not to use MSVC, but if you really want then you might take a look here For Windows & Visual C. You can also think of setting up pyNFFT on your Windows machine. – jojeck May 29 '14 at 16:33
  • I just want to use this library with some other software I've written in c++ using microsoft visual studio. – John May 29 '14 at 16:42
  • The Wikipedia page linked at the top of the answer just describes calculating nonuniform frequency samples of a signal uniformly sampled in time, which was not the original question. Then the inverse problem (reconstructing uniform time samples from unevenly spaced frequency values, which is close to the original question) appears to effectively interpolate the nonuniform spectrum by fitting a Lagrange polynomial, which makes pretty severe assumptions about the nonuniform sampling, e.g. that it is sufficient and has no aliasing. – dpwe Jul 11 '14 at 03:26
  • After Wikipedia: As a result of this, the computed Discrete Fourier Transform can also consist of unevenly sampled frequency values. It is however also possible to compute uniformly sampled frequency values from an unevenly sampled input signal. Now I am bit lost. – jojeck Jul 11 '14 at 12:31