[Ifeffit] parseval's theorem and athena

[Matt Newville]

Regina,

On Fri, Feb 4, 2011 at 10:02 AM,  <kirshstein at googlemail.com> wrote:
> 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