To apply the procedures for the lateral profiling several differentiations must
be calculated. While 
is only interesting for our
model-study, the factors 
occur also when
applying these techniques on experimental data. The discretization error is the
main cause for the noise in the calculated 
and 
characteristics, whereas the numerical error is as a rule negligible.
Particularly critical are the data because the error occurs from
the discretization in time, in addition to the spatial-discretization error.
Note that the relative error is quite small, typically 
for 
,
but sufficient to permit the application of any formula for the numerical
differentiation based on finite differences. For instance, formulas for
numerical differentiation applying finite differences of higher order cannot
be used. In practice, an improved technique for the differentiation of noisy
data has an absolute advantage over the increase of computation accuracy. We
employed cos-convolution
to filter the data. Differentiations are carried out by sin-convolution
applied directly on the raw data. The integrals in G.16
and G.17 applied on a function 
which is known in a
finite number of nonequidistant discrete points allow analytical solutions
when 
is interpolated in the integration interval. In these cases,
both integrals reduce to finite sums. A kind of interpolation between points
on the real axis play an important role. A step-like approximation
cannot be used. When assuming a linear interpolation between neighbouring
points, the analytical solutions of G.16
and G.17 provide proper results. In particular, they enable
exact results for constant 
and linear
. For linear interpolation,
formula G.17 reduces to
where 
, 
,
and 
for 
(if 
). 
and 
denote the first left and right indices with
respect to the integration interval: 
and
, respectively. All differentiations done in this
study have been carried out by G.18.
