Sparse Fourier Transform (SFT) algorithms constitute a transformative approach to spectral analysis by leveraging the inherent sparsity of signals in the frequency domain. In contrast to the ...

A new algorithm performs Fourier transforms using a minimal number of samples. The fast Fourier transform, one of the most important algorithms of the 20th century, revolutionized signal processing.

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 ...

This paper introduces new techniques for the efficient computation of a Fourier transform on a finite group. We present a divide and conquer approach to the computation. The divide aspect uses ...

Researchers have developed a new algorithm that, in a large range of practically important cases, improves on the fast Fourier transform. Under some circumstances, the improvement can be dramatic -- a ...

The Fast Fourier Transform (FFT) is a widely used algorithm that computes the Discrete Fourier Transform (DFT) using much fewer operations than a direct implementation of the DFT. FFTs are of great ...

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 ...