The Fourier transform in analytical science

Abstract

Numerous data analysis methodologies depend on the Fourier transform (FT), especially in analytical chemistry. The FT is a potent and versatile tool, influencing many scientific disciplines. Despite its prominence, the FT is often an enigma for many. In response, this Primer aims to provide an all-encompassing elucidation of the FT for readers not well versed in advanced mathematics. The article explores the theoretical underpinnings of the FT, alongside practical applications, to demystify the fundamental concepts of the method. Its utility is demonstrated through diverse examples, such as mass spectrometry, NMR, infrared spectroscopy and other analytical techniques. Potential extensions of the FT are explored, including potential future developments. The Fourier transform is a mathematical tool for analysing signals that vary in space or time via a transform into the frequency domain. This Primer explores how the Fourier transform is used in analytical science, particularly for spectroscopic data, with an overview of theoretical and experimental considerations.