[Ifeffit] parseval's theorem and athena

Matt Newville newville at cars.uchicago.edu
Thu Feb 17 10:21:20 CST 2011


Hi Regina,

It uses R = [15, 25] Ang by default, though these can be changed with
the "rwgt1" and "rwgt2" parameters to the chi_noise() command.

The normalization definitions can be confusing for discrete transforms
and also given that for the XAFS sin(2kR) one could either choose
conjugate variable pairs of 2k and R or k and 2R (ifeffit uses the
latter).  See  http://cars9.uchicago.edu/~ifeffit/refman/node141.html
for more details.

Using the chi_noise() command, you will typically see small influences
on the exact value of the estimated uncertainty in chi(k) as you
change the FT k-ranges and especially k-weight.   Typically (or at
least, when I look) the order of magnitude (and even the first
significant digit) is generallly preserved.   To be honest, reading
further than 1 significant digit of an automated estimation of noise
based on an assumption of white noise may not be very robust.

Hope that helps,

--Matt




On Thu, Feb 17, 2011 at 8:23 AM,  <kirshstein at googlemail.com> wrote:
> Dear Matt and dear other readers,
>
> I tested the method Matt suggested to make Athena put out the epsilon_k
> value for my data.
> As of itself, the methods works (I get a value), but this value is similar
> but not exactly the same value as I obtain from calculating by myself
> according to parseval's theorem.
> Which makes me think that the small discrepancy might be due to the fact
> that Athena considers a different R-range from what I used (all other
> parameters being the same)?
> I used R 15 to 30 Å. Does someone know what R-range Athena uses?
> Also, just to be sure: so the  normalization used for FFT by Athena is
> sqrt(delta_k / Pi)?
>
> thank you for your kind help,
>
> regina
>
>
> On Fri, Feb 4, 2011 at 8:34 PM, Matt Newville <newville at cars.uchicago.edu>
> wrote:
>>
>> 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
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>
>
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