[Ifeffit] Re: Independent data poins in Artemis
Scott Calvin
SCalvin at slc.edu
Thu Jan 4 13:57:34 CST 2007
Hi Han,
Although I think the basic principle at work here is to be
conservative with your estimate of the number of independent points,
I can still give a couple of replies to this last post.
--Is Dk properly zero in your example? You don't really have a
delta-function, as your measurement of k is not arbitrarily sharp.
With a realistic range of data, that's not an issue of great
importance, but it does impact your argument.
--In a qualitative sense, does a single point in k-space yield any
EXAFS information? I think not. EXAFS is an oscillatory phenomenon.
You can make no estimate of periodicity from a single point, and thus
the Fourier transform, while mathematically computable, doesn't
really have any information that can be used in an EXAFS analysis.
(Another way to put this is to point out that Fourier transforms on
finite intervals always have "truncation effects." The Fourier
transform of a delta function is in some sense entirely truncation
effect, with no information on the signal.)
--Scott Calvin
Sarah Lawrence College
At 12:48 PM 1/4/2007, you wrote:
>I have checked the Matt's note.
>Although I understand the problem, it is still not clear for me.
>If we have only one data point in k-space, it is a delta function.
>For 2DrDk/pi, it should be zero.
>When we do Fourier transformation of the one data point, we still
>have data points in real and imaginary r-space. That is not zero.
>
>Han.
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