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Re: nonuniform FFT [message #34695 is a reply to message #34691]

Mon, 07 April 2003 00:09

MKatz843
Messages: 98
Registered: March 2002

Member

b_gom@hotmail.com (Brad Gom) wrote in message
> has anyone out there implemented a FFT routine that handles
> nonuniformly gridded samples?

If your samples aren't uniformly gridded, I'm not sure how you're
going to get an "FFT" to work. However, there's no reason why you
can't implement a simple (discreet) Fourier Transform minus the "fast"
part.

If you know your non-uniform x values, then for arbitrary k values you
could always Fourier transform your input array, A, like this

i = complex(1,0)
f_k = total( A * exp( i*k*x) )

That's just one Fourier component, and one dimension for x, but
scaling that is trivial.
Of course, computing the FT in this way, one component at a time,
should probably be called a SFT (Slow Fourier Transform).

Depending on your input/output needs, you may be able to implement a
DFT (Discreet Fourier Transform) using IDL's vector/matrix math and
then it can be Much faster. You have a vector of x values where you've
sampled A. You have a vector of k values where you want to know the
Fourier components. If memory serves, the outer product of those two
vectors gives a matrix which is the k*x part of exp(i * k*x). The
proper matrix multiplication by the input array A can yield your FT in
a jiffy--much faster than using a for-do loop.

MKatz843

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[Message index]

		Re: nonuniform FFT By: b_gom on Tue, 08 April 2003 11:26
		Re: nonuniform FFT By: b_gom on Tue, 08 April 2003 11:04
		Re: nonuniform FFT By: stevenj on Mon, 07 April 2003 12:57
		Re: nonuniform FFT By: b_gom on Mon, 07 April 2003 12:09
		Re: nonuniform FFT By: John Smith on Mon, 07 April 2003 11:47
		Re: nonuniform FFT By: James Kuyper on Mon, 07 April 2003 07:10
		Re: nonuniform FFT By: AJ on Mon, 07 April 2003 07:20
		Re: nonuniform FFT By: MKatz843 on Mon, 07 April 2003 00:09

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