The Fourier Transform in Analytical Chemistry*

a review by Marc-André Delsuc & Peter O'Connor

Abstract

Numerous data analysis methodologies heavily depend on the Fourier transform (FT), especially within analytical chemistry. FT is an incredibly potent and versatile tool, significantly influencing various scientific disciplines. Despite its prominence, FT often shrouds itself in an enigma for many. In response, we endeavour to provide an all-encompassing elucidation of FT, crafted to be comprehensible even to those not versed in advanced mathematics. This exposition embraces FT's theoretical underpinnings and practical applications, seeking to demystify this concept. Its utility is demonstrated through examples in diverse domains, such as Mass spectrometry, Nuclear Magnetic Resonance (NMR), Infrared spectroscopy, and various other analytical techniques. Furthermore, potential extensions and applications of FT are explored, evoking the potential future developments of this formidable analytical instrument. We aim to empower novice and seasoned researchers with the knowledge and insight needed to harness FT's transformative capabilities in their scientific pursuits.

This is the submitted version, the final version has been published in Nature Reviews Methods Primers in July 2024

DOI: 10.1038/s43586-024-00326-2

Files organisation

The reference text is Fourier-R2.pdf

There is also an html version, (get also the Fourier-Rev1-02_files folder)

The text is produced with the quarto program

• The *.qmd file is the master document
• the *.py files are used to produce the figures
• bibliography is done with the *.bib and *.csl files
• rendering is available in html and pdf (pdf using the titlepage extension)