Metrohm Vision – Theory - Manual (Page 11)

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2
Math Pretreatment Methods
2.1 N-Point Smooth
This is a boxcar type of smoothing. The method’s parameter, segment size, defines the size of the
boxcar in nanometers. The average spectral value over the segment is placed in the middle in the
segment.
The actual number of data points s in a segment can be calculated from the following equation:
Where x is the declared segment size, ODD is a function that rounds its argument up to the
( ) [ ]
1 2 / ) 3 ( − + = x INT ODD s
nearest odd integer, and INT is a function that rounds its argument down to the nearest integer.
A consequence of the equation for s is that a smooth value cannot be calculated for a certain number
of data points at the beginning and the end of a spectrum. This is so because a number of data
points on each side of a central data point are used in the calculation of an average value for the
segment. Those data points are not available for model development. The number of points “lost” at
each end of the spectrum is given as:
s − 1
2
2.2 First Derivative
The first derivative is used most commonly to eliminate baseline offset variation within a set of
spectra. As a constant (zero order) term added to a function f(w) (the spectrum), offset C is
eliminated by taking the derivative with respect to w (wavelength):
[ ]
) (' ) ( w f C w f
dw
d
= +
While a different offset value C; is associated with each spectrum f(w); all are eliminated in the first
derivative.
Spectral offset may vary within a set of spectra for many reasons including:
• Particle size differences among samples
• Varying particulate levels between liquid samples
• Small changes in instrument response due to short term variation in lamp intensity, detector
response, or instrument temperature
2.2.1 Calculation of the First Derivative
One way to calculate the first derivative is as the first order finite-difference derivative. This method
requires two values to be specified: the length of the segment (segment size); and the length of
the gap between segments (gap size).
The first derivative calculation begins by identifying two segments of the specified size at one end of
the spectrum with a gap between them of the specified size. Next, the average absorbance values
within the first and second segments (A and B, respectively) are calculated. Finally, the first derivative