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Thread Subject:
Non-Uniform Fast Fourier Transform

Subject: Non-Uniform Fast Fourier Transform

From: Ashkan

Date: 11 Nov, 2011 00:26:30

Message: 1 of 8

Hi All,

Does anybody know how I can find fast fourier transform of irregularly distributed data as below:

time velocity
1 0.5
3 0.8
4 0.6
8 0.7
9 0.4

Thank you
Ashkan

Subject: Non-Uniform Fast Fourier Transform

From: Greg Heath

Date: 11 Nov, 2011 06:52:02

Message: 2 of 8

On Nov 10, 7:26 pm, "Ashkan " <a.javadzade...@gmail.com> wrote:
> Hi All,
>
> Does anybody know how I can find fast fourier transform of irregularly distributed data as below:
>
> time    velocity
> 1         0.5
> 3         0.8
> 4         0.6
> 8         0.7
> 9         0.4
>
> Thank you
> Ashkan

1. Interpolate onto a uniform grid and use the FFT.
2. Use and/or modify my DFTgh6 (slow)
3. Use the Lomb-Scargle Algorithm (slow).

Search this group for details of 2 and 3.

Hope this helps.

Greg

Subject: Non-Uniform Fast Fourier Transform

From: Matt J

Date: 11 Nov, 2011 14:44:13

Message: 3 of 8

"Ashkan " <a.javadzadegan@gmail.com> wrote in message <j9hq3m$7id$1@newscl01ah.mathworks.com>...
> Hi All,
>
> Does anybody know how I can find fast fourier transform of irregularly distributed data as below:
===============

This library contains NUFFT code, but I've never used it:

http://www.eecs.umich.edu/~fessler/code/index.html

Subject: Non-Uniform Fast Fourier Transform

From: Greg Heath

Date: 12 Nov, 2011 19:16:28

Message: 4 of 8

On Nov 11, 9:44 am, "Matt J " <mattjacREM...@THISieee.spam> wrote:
> "Ashkan " <a.javadzade...@gmail.com> wrote in message <j9hq3m$7i...@newscl01ah.mathworks.com>...
> > Hi All,
>
> > Does anybody know how I can find fast fourier transform of irregularly distributed data as below:
>
> ===============
>
> This library contains NUFFT code, but I've never used it:
>
> http://www.eecs.umich.edu/~fessler/code/index.html

I wasn't able to use that site.

There is also

http://www-user.tu-chemnitz.de/~potts/nfft/

However, I recall that I had to modify it to get
what I wanted. Unfortunately my results are
on another computer which is currently
dysfunctional.

Greg

Subject: Non-Uniform Fast Fourier Transform

From: TideMan

Date: 12 Nov, 2011 19:52:34

Message: 5 of 8

On Nov 12, 3:44 am, "Matt J " <mattjacREM...@THISieee.spam> wrote:
> "Ashkan " <a.javadzade...@gmail.com> wrote in message <j9hq3m$7i...@newscl01ah.mathworks.com>...
> > Hi All,
>
> > Does anybody know how I can find fast fourier transform of irregularly distributed data as below:
>
> ===============
>
> This library contains NUFFT code, but I've never used it:
>
> http://www.eecs.umich.edu/~fessler/code/index.html

My reading of the abstract is that NUFFT is for non-uniform frequency
spacing, not non-uniform time spacing.

Subject: Non-Uniform Fast Fourier Transform

From: Matt J

Date: 12 Nov, 2011 23:28:11

Message: 6 of 8

TideMan <mulgor@gmail.com> wrote in message <e2d0675d-977e-48ae-8aca-fb75f9fc1566@f29g2000yqa.googlegroups.com>...
>
> > This library contains NUFFT code, but I've never used it:
> >
> > http://www.eecs.umich.edu/~fessler/code/index.html
>
> My reading of the abstract is that NUFFT is for non-uniform frequency
> spacing, not non-uniform time spacing.
===================

That would make sense. It was designed for MRI. However, shouldn't it be applicable to non-uniform time spacing as well, just by virtue of time-frequency duality?

Subject: Non-Uniform Fast Fourier Transform

From: Matt J

Date: 12 Nov, 2011 23:54:19

Message: 7 of 8

"Matt J" wrote in message <j9mveb$ohl$1@newscl01ah.mathworks.com>...
>
> > My reading of the abstract is that NUFFT is for non-uniform frequency
> > spacing, not non-uniform time spacing.
> ===================
>
> That would make sense. It was designed for MRI. However, shouldn't it be applicable to non-uniform time spacing as well, just by virtue of time-frequency duality?
======================

I guess not, judging by example_nufft1_reverse.m in the library. Oh well...

Subject: Non-Uniform Fast Fourier Transform

From: Bill Whiten

Date: 13 Nov, 2011 05:04:10

Message: 8 of 8

"Ashkan " <a.javadzadegan@gmail.com> wrote in message <j9hq3m$7id$1@newscl01ah.mathworks.com>...
> Hi All,
>
> Does anybody know how I can find fast fourier transform of irregularly distributed data as below:
>
> time velocity
> 1 0.5
> 3 0.8
> 4 0.6
> 8 0.7
> 9 0.4
>
> Thank you
> Ashkan

You could try it as a regression problem, regress against time transformed to sin and cos of the frequencies you are interested in. If you have a lot of data and frequencies you will see why it is called the Fast Fourier transform.

Regards

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