[Ifeffit] Fwd: Re: Independent data poins in Artemis
bravel at anl.gov
Thu Jan 4 15:49:29 CST 2007
Whoops! I just sent this to Han earlier and meant to send it to the
whole list. Silly me!
---------- Forwarded Message from Bruce Ravel <Bruce Ravel
<bravel at anl.gov>> ----------
Subject: Re: Independent data poins in Artemis
Date: Thursday 04 January 2007 14:50
From: Bruce Ravel <bravel at anl.gov>
To: "Sang-Wook Han" <swhan at chonbuk.ac.kr>
On Thursday 04 January 2007 11:48, Sang-Wook Han 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.
This question and the other answers to it are all charmingly pedantic
with regards to the formalism of measurement theory ;-) The main
point, IMHO, is that the Nyquist criterion is only true for a properly
packed signal. EXAFS resembles a sum of sine waves, but is *not*, in
fact, a sum of pure sines waves. The Nyquist criterion, then, is a
statement about the maximum possible amount of information in your
data, but does not tell you the amount of information that you
actually have. Quantifying the information content of an improperly
packed signal is the point of the Baysian approach that Scott
discussed in in his earlier message. The bottom line is that real
EXAFS data tends to have somewhat less than Nidp independent points.
One could apply Baysian formalism. Or one could be conservative in
the use of parameters and mindful of the level of correlation between
parameters. In either case, asserting +0, +1, or +2 in your statement
of the Nyquist criterion is pedantry. Indeed, by focussing on that
fairly trivial aspect of formal information theory, you are missing a
much more improtant point about your real EXAFS measurement.
Bruce Ravel ---------------------------------------------- bravel at anl.gov
Molecular Environmental Science Group, Building 203, Room E-165
MRCAT, Sector 10, Advanced Photon Source, Building 433, Room B007
Argonne National Laboratory phone and voice mail: (1) 630 252 5033
Argonne IL 60439, USA fax: (1) 630 252 9793
My homepage: http://cars9.uchicago.edu/~ravel
EXAFS software: http://cars9.uchicago.edu/~ravel/software/
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