BUCHI NIRCal - Manual (Page 118)

NIRCal 5.5 Software Manual
118 NIRCal 5.5 Manual, Version A
Reciprocal
Formula:
Type
This pretreatment is not depending on the calibration wavelengths.
3.5.8 Filter
Linear Filter
Linear filters allow the application of user defined pretreatments. For instance it is possible to apply
average smoothing, derivative, low and high band pass filtering. The default linear filter in NIRCal
contains a neutral setting of 1, 1.
It is best to show examples for the explanation of linear filters.
The coefficients for the lienar filter will be explained for a Savitzky-Golay first derivative. In the original
paper (Anal. Chem. 36, 1627-1639 (1964) the following formula was given using orthogonal cubic
polynomes (nine points):
This formula will be transferred into the following coefficients for linear filters:
-86, 142, 193, 126, 0, -126, -193, -142, 86, 1188
The coefficient for the highest x-value x(i+4) is
–86, for the lowest x-value x(i-4) the coefficient is +86.
The coefficient is 0 for that term, where there is no contribution; in this example it is in the middle, i.e.
x(i+0). The last value of the coefficients is the Scale Factor. The sum will be divided by the scale
factor.
As next example a three point average smoothing is used. The formula is:
x'(i) = ( x(i+1) + x(i) + x(i-1) ) / 3
The corresponding coefficients for this example are: 1, 1, 1, 3