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# Interpolation details

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 resolution of a spectrum can be changed.

• Data points can be shifted on the x-axis.

• Cut a spectrum.

## Change resolution

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.

## Change Resolution Example

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: ## Shift x-axis data points

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.

## Shift x-axis data points example

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: After shifting, the spectrum looks like this: ## Cut spectrum

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.