Norton-Beer apodization and its Fourier transform.

Area of Science:

• Spectroscopy
• Computational Chemistry
• Signal Processing

Background:

• Apodization in Fourier transform spectroscopy is crucial for modifying instrument line shapes and minimizing side lobe artifacts.
• Norton-Beer apodization functions are widely adopted due to their effectiveness in Fourier transform spectroscopy applications.
• Existing methods for calculating the Fourier transform of Norton-Beer functions are limited to a specific subset of these functions.

Purpose of the Study:

• To develop a general analytical method for computing the Fourier transform of any Norton-Beer apodization function.
• To introduce a free Python library, norton_beer, that implements the analytical solution for generating apodization windows and their Fourier transforms.
• To enable the creation of new Norton-Beer apodization functions tailored to specific spectral resolution requirements.

Main Methods:

• Derivation of a general analytical solution for the Fourier transform of all Norton-Beer apodization functions.
• Development of the norton_beer Python library, incorporating the derived analytical solution.
• Implementation of functions for generating apodization windows and their corresponding Fourier transforms.

Main Results:

• A universally applicable analytical method for the Fourier transform of Norton-Beer apodization functions has been established.
• The norton_beer Python library provides a practical tool for spectroscopists to utilize these analytical solutions.
• The library supports the generation of custom Norton-Beer functions for optimized spectral resolution.

Conclusions:

• The presented general method and the norton_beer library significantly advance the application of Norton-Beer apodization in Fourier transform spectroscopy.
• This work facilitates more precise control over instrument line shapes and spectral analysis.
• The availability of these tools empowers researchers to design apodization strategies for specific spectroscopic needs.