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# Normalization details

Normalize is used to scale the intensity values of a 2D or 3D data object within user defined limits. Usually this function is useful for visual comparison of two or more 2D data objects. It is also required as pre-processing function for many other mathematical functions even in chemometric analysis or colorimetric analysis. Data might be normalized to an absolute user defined intensity interval or the current y-offset is kept. The latter is called relative normalization.

## How does normalize work?

All intensities of the 2D or 3D data object will be corrected using a scaling factor f to fit data to the user defined borders of the new intensity interval. The scaling factor f will be derived from the current global minimum Imin and maximum Imax Intensities and the new user defined minimum Iâmin and maximum Iâmax intensities of the 2D data object as follows:

Each intensity Ii of the 2D or 3D data object is then recalculated to fit the new interval using a linear transformation:

## Normalize parameters

The following normalize parameters might be adjusted:

### Minimum Y

The Minimum Y parameter is only used, if the Normalize Minimum flag is set true. It holds the new lower bound of the intensity interval. After normalization, the lowest intensity within the 2D or 3D data object is scaled to the Minimum Y value.

### Maximum Y

The Maximum Y parameter is always applied. It holds the new upper bound of the intensity interval. After normalization, the highest intensity within the 2D or 3D data object is scaled to the Maximum Y value.

### Normalize minimum

Two types of normalizations can be applied:

• Absolute normalization
Data is scaled within the user defined interval between Minimum Y and Maximum Y values. After normalization, the lowest intensity value in the 2D or 3D data object is equal to the Minimum Y value and the highest observed intensity value is equal to Maximum Y.

• Relative normalization
This procedure considers the current y-offset of the 2D or 3D data object that will be kept. Data is scaled between a user defined interval starting with the lowest available intensity in the spectrum and ending with Maximum Y value. The Minimum Y value is ignored in this case.