Relationship of Fourier transforms to isotope distribution calculations

Abstract

Abstract Isotope distributions of molecules are the result of convoluting elemental isotope distributions multiple times. They are usually calculated using a polynomial expansion method. The present paper starts with the polynomial expansion and shows how to cast the problem in terms of Fourier transforms. Because discrete Fourier transforms can be calculated very efficiently, this new way of looking at the problem has significant practical implications. Specifically, it leads to faster ways to calculate isotope distributions.