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 ...
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 ...
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 ...
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 ...
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, ...
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