Regina,
On Fri, Feb 4, 2011 at 10:02 AM,
Hello,
I would like to use parseval's theorem (as described in a document called: Error Reporting Recommendations: A Report of the Standards and Criteria Committee, Adopted by the IXS Standards and Criteria Committee July 26, 2000 ) to quantify the statistical noise in my spectra.
In section 3 (as shown in the attachment), it says that for the formula to work, the forward FT has to be normalized by sqrt(deltak/Pi). (delta k is the spacing of points in k space)
What is the normalization used for FFT in athena? if it is not sqrt(deltak/Pi), what is it? how does the parseval theorem formula need to be modified as a function of FT normalization?
Many thanks for answers!
Regina
It's even easier than that. Ifeffit / Artemis do (and Athena can) report the epsilon_k and epsilon_r as defined in that report. The 2000 report actually codified work done with the earlier feffit code to estimate the noise in the data in both k and R space. Again, Artemis does this automatically, and you can see the values for epsilon_k and epsilon_r when looking at fit results. Athena doesn't directly do this calculation, but if you open the Ifeffit Buffer (Edit -> Display Ifeffit Buffer), you can do the following: 1. choose FFT parameters in the Forward Fourier transform part of the main Athena window. 2. Hit the [R] Plot button for the group of data you're looking at to make sure the FFT parameters are up to date. 3. Open up the Ifeffit Buffer and look for the "Group Name" (Athena uses a 4 letter sequence which looks random). You'll see something like newplot(jukc.k, "(1*jukc.chi*jukc.k^2)+0.0000", ....) All you're looking for is the 4-letter "Group Name" / prefix for the data set: in this case "jukc" 4. In the Ifeffit> input line at the bottom of the buffer, type chi_noise(jukc.chi) 5. Then type show epsilon_k, epsilon_r This will show the values estimated for the noise in chi(k) and chi(R) using the FFT parameters you input. For most data and FFT parameters, epsilon_k should not change significantly, though epsilon_r will change significantly with the k-weight. Cheers, --Matt