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 ...

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 ...

Design linear discrete-time systems and filters and analyze their behavior. Represent continuous-time signals and linear systems in discrete time, so that such signals can be recovered in continuous ...

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 ...

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 ...

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

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 ...