Norton-Beer apodization and its Fourier transform

Abstract

In Fourier transform spectroscopy, apodization is used to alter the instrument line shape, reducing the prominence of its side lobes. The Fourier transform of the apodization window is of great interest as it allows us to compute or optimize the line shape. In the last decades, many apodization windows have been proposed, from which the group of Norton-Beer apodization functions gained large popularity in Fourier transform spectroscopy. While for a small set of specific Norton-Beer apodization functions analytical solutions of the Fourier transform have been presented in the past, we present here a general method, which allows us to calculate the analytical solution of the Fourier transform for any Norton-Beer apodization function. This paper also documents the free Python library called norton_beer. It contains functions to generate apodization windows and their Fourier transform following the presented analytical solution. Furthermore, new Norton-Beer apodization functions can be generated for any desired spectral resolution.