GBS Elektronik MCA166-USB User Manual
Page 33
Centroid:
The peak centroid is the sum of the channel contents
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
2
1
1
2
'
+
+
−
−
+
+
+
+
=
i
i
i
i
i
i
Spectrum
Spectrum
Spectrum
Spectrum
Spectrum
Spectrum
where,
Spectrum
i
- the original contents of channel i
Spectrum
i
'
- the smoothed contents of channel i
7 background corrected
33