Suppose the data were tabulated locally on a 0.01A^-1 grid, then sampled on the default 0.05A grid with cubic-spline interpolation. In that case, the spline interpolated value depends mostly on the couple of samples nearest the new grid points, which means that you're not really using all the data equally. I suppose it could be argued, then, that smoothing distributes some of the weight of the 'in-between' points so that they're accounted for, the way boxcar averaging does. What my code does (original idea frpm Brian Kincaid) is a linear weighting, essentially a triangular convolution kernel rather than a rectangle, as in boxcar averaging. Think of it as A-frame averaging rather than boxcar. That's sharper, so would result in less loss of amplitude in the high shells. If you have a distance of 5A, then the phase shift between .05A^-1 gridpoints is 0.5rad. At the top of a wiggle, you're essentially averaging cos(phi) over the range [-0.25,0.25], which gives you an amplitude of sin(0.25)/0.25 = 0.98. Thus, I don't understand how boxcar averaging makes a noticeable difference here except for really long paths. For a triangular average over a phase range +-delta, the relevant amplitude reduction is f = Integrate[Cos[phi]*(1 - phi/delta), {phi, 0, delta}]/Integrate[(1 - phi/delta), {phi, 0, delta}] (Mathematica notation, using symmetry of the functions) which comes to f = 2(1-Cos(delta))/delta^2, whose leading term is 1-delta^2/12. Thus, to lose 10% of the amplitude, delta would have to be about 1.12rad, which means a phase shift between grid points of 2.24rad, thus a distance of 22A. A caveat: This derivation only covers the phase. Presumably, an amplitude varying with k would cause a phase shift of the averaged wave. I haven't worked out how bad that might be. The triangular kernel assigns the full weight of each input point to some combination of the new grid points on each side, so nobody's left out. mam On 4/21/2017 3:36 PM, Christopher Thomas Chantler wrote:

�� I'm just agreeing with Matt's comment.

Too fine a spacing does not help you due to typical broadening from imfp or thermal sources [or structural disorder].

And the difference between operation of ifeffit and larch in this context is pretty interesting.

-------------------------------------------------------------------------------------- Christopher Chantler, Professor, FAIP, Fellow American Physical Society Editor-in-Chief, Radiation Physics and Chemistry Chair, International IUCr Commission on XAFS President, International Radiation Physics Society School of Physics, University of Melbourne Parkville Victoria 3010 Australia +61-3-83445437 FAX +61-3-93474783 chantler@unimelb.edu.au https://owa.unimelb.edu.au/owa/redir.aspx?C=c7BoS0kVVkC1_S95-9x9l5cBu6YTjdAITgSrfUpfDAUV5oUH1LFYBcz08w8xvHMJoosZRdagfQM.&URL=mailto%3achantler%40unimelb.edu.au chantler@me.com https://owa.unimelb.edu.au/owa/redir.aspx?C=c7BoS0kVVkC1_S95-9x9l5cBu6YTjdAITgSrfUpfDAUV5oUH1LFYBcz08w8xvHMJoosZRdagfQM.&URL=mailto%3achantler%40me.com http://optics.ph.unimelb.edu.au/~chantler/xrayopt/xrayopt.html https://owa.unimelb.edu.au/owa/redir.aspx?C=c7BoS0kVVkC1_S95-9x9l5cBu6YTjdAITgSrfUpfDAUV5oUH1LFYBcz08w8xvHMJoosZRdagfQM.&URL=http%3a%2f%2foptics.ph.unimelb.edu.au%2f%7echantler%2fxrayopt%2fxrayopt.html http://optics.ph.unimelb.edu.au/~chantler/home.html https://owa.unimelb.edu.au/owa/redir.aspx?C=c7BoS0kVVkC1_S95-9x9l5cBu6YTjdAITgSrfUpfDAUV5oUH1LFYBcz08w8xvHMJoosZRdagfQM.&URL=http%3a%2f%2foptics.ph.unimelb.edu.au%2f%7echantler%2fhome.html

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ *From:* Ifeffit on behalf of ifeffit-request@millenia.cars.aps.anl.gov *Sent:* Friday, 21 April 2017 11:01:11 PM *To:* ifeffit@millenia.cars.aps.anl.gov *Subject:* Ifeffit Digest, Vol 170, Issue 21

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Today's Topics:

1. Re: Ifeffit Digest, Vol 170, Issue 19 (Matt Newville) 2. Fwd: Ifeffit Digest, Vol 170, Issue 19 (Matt Newville) 3. Looking for EXAFS data of Ni2+ ion in aqueous solution (Van Vu)

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Message: 1 Date: Thu, 20 Apr 2017 21:18:39 -0500 From: Matt Newville To: XAFS Analysis using Ifeffit Subject: Re: [Ifeffit] Ifeffit Digest, Vol 170, Issue 19 Message-ID: Content-Type: text/plain; charset="utf-8"

Hi Chris,

On Thu, Apr 20, 2017 at 5:02 PM, Christopher Thomas Chantler < chantler@unimelb.edu.au> wrote:

...

Note that in general any and every smoothing operation reduces the information content of the data and its ability to reveal structure.

Well, maybe. If one has mu(E) measured every 0.01 eV over an 600 eV EXAFS scan to k=12A^-1, one does not really 60,000 independent measures of the structure. Yuji's data wasn't that absurd, but it did have close to 4000 measurements for the full EXAFS spectrum out to k=18^-1. And to be clear, there is not anything wrong with that, it's just a matter of how you decide to treat it.

As the plots attached in Yuji's original message and my replies show, the resulting chi(k) definitely has is amplitude suppressed when doing a simple boxcar average of data onto the 0.05 Ang^-1 grid (Athena with Ifeffit). But when using cubic spline interpolation (Larch), the amplitude of the EXAFS oscillations are not noticeably suppressed, though the high frequency noise is also much higher. Applying a Savitzky-Golay filter prior to the cubic spline interpolation did not appreciably suppress the EXAFS oscillations though the high frequency noise was reduced.

Very finely-spaced energy data might reveal is at much higher R than we can hope to model with EXAFS. A k-grid of 0.05 Ang^-1 can give frequencies to 31Ang, and so is probably accurate to 16Ang without significant signal loss. That is, out to k=18Ang^-1, you really only need 360 samples, but you'd like these as noise-free as possible. Having 3600 measurements on a grid of 0.005 Ang^-1 might give you data out to 160Ang in principle, but the photo-electron tends to not cooperate.

--Matt