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Re: IDL 5.5, 2D FFT indexing confusion. [message #44825 is a reply to message #44821]

Tue, 19 July 2005 09:44

Pitufa
Messages: 8
Registered: July 2005

Junior Member

Thanks for your reply, I was wondering if there was a way to shrink the
phi derivation!

About the symmetry in fft, here is why I thought it had to be point
symmetric about the centre. The FFT of a function f_{kj} is given by
(for a square array of side dimension N):

F_{m,p} = (1/N^2) sum_{k,j} f_{k,j} exp[-2pi i (km + jp)/N] eqn.
[1]

Now, if the array in fourier space has its origin at the centre of the
array, then the point (m, p) is centrally opposite to (N-m, N-p). And
the FFT for this point is:

F_{N-m,N-p} = (1/N^2) sum_{k,j} f_{k,j} exp[-2pi i (k(N-m) + j(N-p))/N]
= (1/N^2) sum_{k,j} f_{k,j} exp[2pi i (km + jp)/N] exp[-2pi i (k+ j)]
= (1/N^2) sum_{k,j} f_{k,j} exp[2pi i (km + jp)/N] eqn. [2]

which is the complex conjugate of eqn [1] if f_{k,j} is real.

Please let me know if you don't agree.

Thanks,

Pitufa.

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[Message index]

		Re: IDL 5.5, 2D FFT indexing confusion. By: R.G. Stockwell on Tue, 19 July 2005 13:49
		Re: IDL 5.5, 2D FFT indexing confusion. By: Pitufa on Tue, 19 July 2005 09:44
		Re: IDL 5.5, 2D FFT indexing confusion. By: Benjamin Hornberger on Tue, 19 July 2005 07:29
		Re: IDL 5.5, 2D FFT indexing confusion. By: Pitufa on Thu, 21 July 2005 10:28

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