[Ifeffit] Re: Independent data poins in Artemis

[Scott Calvin]

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.