Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, ...

The Fourier transform (FT), a cornerstone of optical processing, enables rapid evaluation of fundamental mathematical operations, such as derivatives and integrals. Conventionally, a converging lens ...

A talk, The Unreasonable Effectiveness of the Fourier Transform, was presented by [Joshua Wise] at Teardown 2025 in June last year. Click-through for the notes or check out the video below the break ...

BELLINGHAM, Washington, USA - Joe Goodman, an international expert in Fourier optics, statistical optics, and speckle phenomena, has published his latest book, Fourier Transforms Using Mathematica®, ...

In this article, we derive a series expansion of the multivariate normal probability integrals based on Fourier series. The basic idea is to transform the limits of each integral from hi to ∞ to be ...

The linear canonical transform (LCT) is a versatile integral transform that generalises classical transforms such as the Fourier, fractional Fourier, and Fresnel transforms. By utilising four ...

In the last twenty years there have been many connections discovered between fractal geometry and harmonic analysis. One such connection is a Fourier transform formula for the energy integral of a ...

This monthly journal, published since 1900, is devoted entirely to research in pure and applied mathematics, and, in general, includes longer papers than those in the Proceedings of the American ...

In less than 100 seconds, Carola-Bibiane Schönlieb of the University of Cambridge in the UK provides a basic definition of a Fourier transform. She explains how this mathematical tool was introduced ...