Braun MCA166-USB user manual Centroid, Smooth

Centroid:

The peak centroid is the sum of the channel contents7 times the channel number divided by the sum of the channel contents in the range of the channels above the half maximum:

	∑ h	i * Spectrum
Centroid =	i= l	i
	h
	∑ Spectrumi

i= l

where,

i = channel number

Spectrumi = 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 '	= Spectrumi− 1 +		2 * Spectrumi + Spectrumi+ 1
i			4
5 point smoothing:
'	=	Spectrumi− 2 +	4 * Spectrumi− 1 + 6 * Spectrumi + 4 * Spectrumi+ 1 + Spectrumi+ 2
Spectrumi			16
where,
Spectrumi	- the original contents of channel i
Spectrum '	- the smoothed contents of channel i
i

7background corrected

33