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Centroid:
The peak centroid is the sum of the channel contents
7
times the channel number divided by the sum of the
channel contents in the range of the channels above the half maximum:
Centroid =
i Spectrum
Spectrum
i
i l
h
i
i l
h
*
=
=
∑
∑
where,
i
= channel number
Spectrum
i
= net contents of channel i
FWHM:
The Full Width at Half Maximum (FWHM) is the background corrected peak’s width at one-half of its
maximum amplitude. The algorithm first proceeds down one side of the peak until it finds a channel (e.g.
1203) whose counts fall below the half maximum channel. It is now made sure that the following channel (e.g.
1204) also falls below the half maximum channel. The same algorithm is applied for the other side of the
peak. The left and the right FWHM points are the interpolated channels between the counts of the channel
below and above the half maximum value.
Smooth:
Smooth averages the current spectrum (the original data will be overwritten) using a binomial formula:
3 point smoothing:
Spectrum
Spectrum Spectrum Spectrum
i
i i i
'
*
=
+ +
− +
1 1
2
4
5 point smoothing:
16
*4*6*4
2112
'
++−−
++++
=
iiiii
i
SpectrumSpectrumSpectrumSpectrumSpectrum
Spectrum
where,
Spectrum
i
- the original contents of channel i
Spectrum
i
'
- the smoothed contents of channel i
7 background corrected
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