       FWHM, InterpolationFunction & Solve

• To: mathgroup at smc.vnet.net
• Subject: [mg80418] FWHM, InterpolationFunction & Solve
• From: Mathieu G <ellocomateo at free.fr>
• Date: Wed, 22 Aug 2007 04:39:36 -0400 (EDT)

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.