The interpolation is available
for equidistant and
discrete data. Interpolation
may be used to convert discrete data into equidistant data. It comprises
three different functions at once:
The data point density or resolution of an equidistant 2D data object
can be modified. This is sometimes useful to smooth data or reduce the
resolution for a zero-filling.
According to a new user defined resolution, data points will be adjusted
on the x-axis. The new resolution can be higher or lower than the old
one. Depending on the new resolution settings, the number of data points
is increased or decreased accordingly.
The intensities Ii
at each data point i is then
interpolated using a polynomial fit function Pi with a user
defined degree M similar to the
Savitzky-Golay algorithm. A polynomial degree M
between zero to three and a window of five data points are used for computation
of 0th order, linear, squared
and cubic interpolation. The interpolation polynomial looks like this:
Legend:
Pi
Polynomial fit function
M
polynomial degree
ai
polynomial coefficients
Ii
Intensity at the ith data
point
What does a polynomial degree zero mean?
0th
order interpolation means, that missing data point intensities will be
filled up with the same intensity value of data points nearby.
By changing the resolution, the data point density of a 2D data object
can be increased or decreased. In the following example the data point
density will be decreased by half.
The data points of the 2D data object are displayed as vertical lines
for a better visualization:
After changing the resolution, the 2D data object looks like this:
Sometimes, it is required, that the spectral region is slightly shifted,
e.g. to match the data points of another spectrum.
Within the limits of two times the resolution of the spectrum, the starting
point and ending point of a data object can be shifted. New data point
positions and related intensities are interpolated as described for the
change resolution function.
How far can data points be shifted from their
origin?
Data point shifting is only possible within
the limit of two times the resolution of the 2D data object.
The x-axis of the 2D data object is shifted by -0.5 units
(to the left). The data points of the 2D data object are displayed as
vertical lines for a better visualization:
Sometimes, the user is only interested in a particular spectral region.
Exceeding data points can be removed just by cutting the spectrum on the
left or right side of the x-axis. The interpolation
function lets the user choose new borders for the spectrum.
Cutting can also be done using the Cut
X-Axis command. For
details please refer to the chapter "Commands".
How can I set new borders of a spectrum?
Enter a new starting value and / or new
ending value within the current spectrum borders in the interpolation
function and the spectrum will be cut according to the new borders.
