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 ...

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 ...

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

This paper describes the "fractional Fourier transform," which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier ...