Re: FWHM, InterpolationFunction & Solve

• To: mathgroup at smc.vnet.net
• Subject: [mg80530] Re: FWHM, InterpolationFunction & Solve
• From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
• Date: Fri, 24 Aug 2007 02:04:05 -0400 (EDT)
• Organization: University of Maryland, Baltimore County
• References: <fagstu\$8du\$1@smc.vnet.net>

```If your data are noisy, I would recommend the use of a Savitzky-Golay
filter. The gist of this is that a polynomial of some degree d is fit
(LSQ) to 2N+1 data points, both d and N are user determined. Then the
middle data point of the 2N+1 is replaced with the curve fit value. The
process proceeds by sliding one point to the right. All of these
operations happen on the original data.

This is a smoothing filter that removes some of the "higher frequency"
stuff on the assumption that it is due to "noise".

I have a NB with some details. If you would like, I could send it to you.

Kevin
Mathieu G wrote:
> Hello,
> I have a set of discrete data, representing a peak.
> I would like to compute the Full Width at Half Maximum (FWHM) of this peak.
> For that I would like to know which points correspond to half the peak value.
> SO far I was considering using an interpolating function, but this does
> not seem to work:
>
>
> DataFile = Import["FFT.dat"];
> CleanDataFile = Part[DataFile, 2 ;; Length[DataFile]];
> WorkingData = CleanDataFile[[All, {1, 3}]];
>
> ListLinePlot[WorkingData, PlotRange -> All]
>
> MaximumFFTY = Max[WorkingData[[All, 2]]];
> MaximumFFTPosition = Position[WorkingData, MaximumFFTY][[1, 1]];
> MaximumFFTX = WorkingData[[MaximumFFTPosition, 1]];
>
> DataInterpolation = Interpolation[WorkingData];
>
> Solve[DataInterpolation[x] == MaximumFFTValue/2, x]
>
>
> Can you help me please? How would you do that?
> I then want to compute the area under the peak:
>
> Integrate[DataInterpolation[x], {x, BegFWHM, EndFWHM}]
>
> Which works fine with the interpolating function.
>
> Thank you for your help!
> Mathieu
>

```

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