MCA527 Algorithm, Formulas
Centroid:
The peak centroid is the sum of the channel contents
9
times the channel number divided by the sum of the
channel contents in the range of the channels above the half maximum:
where
i
= channel number
l
= lowest channel above the half maximum
h
= highest channel above the half maximum
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:
5 point smoothing:
where
Spectrum
i
= the original contents of channel i
Spectrum
i
'
= the smoothed contents of channel i
9 background corrected
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Centroid
=
∑
i
=
l
h
i
⋅
Spectrum
i
∑
i
=
l
h
Spectrum
i
Spectrum
i
'
=
Spectrum
i
−
1
2
∗
Spectrum
i
Spectrum
i
1
4
Spectrum
i
'
=
Spectrum
i
−
2
4
∗
Spectrum
i
−
1
6
∗
Spectrum
i
4
∗
Spectrum
i
1
Spectrum
i
2
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