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 have proved that the lower bound of the number of real multiplications for computing a length 2t real GFT(a,b) (a = ±1/2, b = 0 or b = ±1/2, a = 0) is 2t+1 – 2t - 2 and that for ...

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 ...

The Fourier transform, which splits a complicated signal into individual pure frequencies, was devised over 200 years ago but only became widely used after the development of an algorithm called the ...

This paper presents an efficient methodology for discrete Asian options that is consistent with different types of underlying densities – especially non-normal returns as suggested in the empirical ...

We develop efficient fast Fourier transform algorithms for pricing and hedging discretely sampled variance products and volatility derivatives under additive processes (time-inhomogeneous Lévy ...

A group of MIT researchers believe they’ve found a way to speed up audio, video, and image compression by improving on the Fourier Transform. They say the new algorithm is up to ten times faster than ...

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 ...