BUCHI NIRCal - Manual (Page 119)

Chemometrics
NIRCal 5.5 Manual, Version A 119
Linear filters are very useful when spectra recorded with a different resolution have to be treated
similarly to original spectra with e.g. only one third of data points (step from NIRFlex N-400 to NIRFlex
N-500). For similar prediction results of calibrations smoothing and deriving functions should be
adapted. In the following tables the linear filters for the basic smoothing- and derivative functions are
summarized.
Derivatives
Linear Filter Coefficients
First Derivative BCAP (db1) 1,1,0,-1,-1,4
First Derivative Taylor 3 points (dt1) 1,0,-1,2 {= First Derivative Finite
Differences}
First Derivative Savitzky-Golay 9
points (dg1) -86,142,193,126,0,-126,-193,-
142,86,1188
Second Derivative BCAP (db2) 1,-2,1,2
Second Derivative Taylor 3 points
(dt2) 1,-2,1,2 )*
Second Derivative Savitzky-Golay 9
points (dg2) 28,7,-8,-17,-20,-17,-8,7,28,462
Second Taylor 3 Points Segment5
Gap5 (ds2) 1,1,1,1,1,0,0,0,0,0,-2,-2,-2,-2,-
2,0,0,0,0,0,1,1,1,1,1,5
{Second Derivative Finite Differences
*} {1,0,-2,0,1,1}
Third Derivative Taylor 5 Points (dt3) 1,-2,0,2,-1,2
{Third Derivative Finite Differences} {1,0,-3,0,3,-1,1}
*) due to upward compatibility reasons, identical to BCAP
{…} not included in NIRCal 5; for “Finite Differences” see: Norris and Williams in “NIR-Technology in
Agricultural and Food Industries” p. 48
Smoothing
Linear Filter Coefficients
Average 3 Points (sa3) 1,1,1,3
Average 9 Points (sa9) 1,1,1,1,1,1,1,1,1,9
Savitzky-Golay 9 Points (sg9) -21,14,39,54,59,54,39,14,-21,231
There are various ways for adapting Filters for the step between data of e.g. the NIRFlex N-400 and
NIRFlex N-500. As a simple recipe we suggest to repeat each filter coefficient 3 times and adjust the
scale or insert zero coefficients between the coefficients and also here adjust the scale. The recipe is
illustrated for the second derivative BCAP (db2) below.
Number of data points: 500
Linear Filter Coefficients
500 1,-2,1,2
Various alternatives:
1501 1,1,1,-2,-2,-2,1,1,1,3
1501 1,0,0,-2,0,0,1,1.2
1501 1,0,-2,0,1,0.7
For new NIRFlex N-500 datasets gap2 pretreatements have been introduced with NIRCal 5.2. The
following tables show the linear filter coefficients for gap2 pretreatements.