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Re: possible bug with center keyword option for FFT [message #75040]

Fri, 11 February 2011 12:41

R.G.Stockwell
Messages: 163
Registered: October 2004

Senior Member

"R.G. Stockwell" wrote in message news:ij46h9$cg9$1@speranza.aioe.org...

>
>
> "Mark" wrote in message
> news:babf90b7-e4a3-48bc-aecf-ae81e4a055d4@o18g2000prh.google groups.com...
>
>
> 2: According to the documentation, with the center keyword off in
> FFT(), element(0) is the FFT coefficient for the zero frequency. With
> the keyword center set, this coefficient is shifted to the 'center' of
> the array. This is a little ambiguous, especially when an array might
> have an even or odd number of points in a dimension.

You are absolutely correct. This is an error in IDL.

**********************************************

also, for the odd case, IDL is also wrong.
When there is an odd number of points, the actual nyquist value is not
sampled. (great trick question for anyone who thinks the nyquist is 1/(2T))

so you have, N = 7, and take T = 1 as the sampling interval:
I, freq

0, DC
1, 1/N
2, 2/N
3, 3/N
4, -3/N
5, -2/N
6, -1/N

so the 'centered' fft is:
i, old i, freq

0, 4, -3/N
1, 5, -2/N
2, 6, -1/N
3, 0, DC
4, 1, 1/N
5, 2, 2/N
6, 3, 3/N

From the example shown, the dc went to the 4th index when centered, it MUST
go to the 3rd index.

cheers,
bob

PS, I hope it's obvious how I am writing that. the first number is the
current index of the spectrum array. Then the next column is the "old"
index based on the result of a straight FFT (i.e with out the center
keyword), then the final column is what the frequency value is, of a N point
time series with sampling T = 1, and here N = 7 but I thought that it would
be confusing to write out the 7 each time.

----------------------------
R.G. Stockwell, Ph.D.
Northwest Research Associates,
Colorado Research Associates Div.
3380 Mitchell Lane Boulder CO USA 80301
----------------------------

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[Message index]

		Re: possible bug with center keyword option for FFT By: R.G.Stockwell on Fri, 11 February 2011 12:41
		Re: possible bug with center keyword option for FFT By: R.G.Stockwell on Fri, 11 February 2011 12:34
		Re: possible bug with center keyword option for FFT By: astroboy2k on Fri, 11 February 2011 10:17
		Re: possible bug with center keyword option for FFT By: David Fanning on Fri, 11 February 2011 10:05
		Re: possible bug with center keyword option for FFT By: chris_torrence@NOSPAM on Tue, 15 February 2011 12:25

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