Whoops! I just sent this to Han earlier and meant to send it to the whole list. Silly me! B ---------- Forwarded Message from Bruce Ravel > ---------- Subject: Re: Independent data poins in Artemis Date: Thursday 04 January 2007 14:50 From: Bruce Ravel To: "Sang-Wook Han" 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.

Han, 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. B -- Bruce Ravel ---------------------------------------------- bravel@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/