In this paper we describe a method for computing the Discrete Fourier Transform (DFT) of a sequence of $n$ elements over a finite field $\mathrm{GF}(p^m)$ with a ...

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 ...

Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform? [Shalma] begins by telling you a little about Joseph Fourier, the French mathematician with an interest in heat propagation ...

A key algorithm that quietly empowers and simplifies our electronics is the Fourier transform, which turns the graph of a signal varying in time into a graph that describes it in terms of its ...

Harmonic analysis occupies a central position in modern mathematical analysis by providing the tools to express complex functions as superpositions of simpler sinusoidal components via the Fourier ...

Comprehensive introduction to analysis of continuous and discrete-time signals and systems. Linear time-invariant systems, convolution; Fourier series representations of periodic signals; Continuous ...

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 ...

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, ...

Lie groups provide a natural framework for describing continuous symmetries in both mathematics and physics. These groups, which are simultaneously smooth manifolds, allow for the integration of ...