A differentiable fractional Fourier transform (FRFT) implementation with layers that can be trained end-to-end with the rest of the network. This package provides implementations of both fast ...

Steps of the proof 1. Calculation of Fourier coefficients $$ { \hat {\Delta}_a (n) }$$ and confirmation of the sign First, to confirm the hint " $$ { \hat {\Delta}_a (n) \ge 0 }$$ ", we calculate the ...

Researchers from the University of Cambridge and GlitterinTech, a startup founded by the same research group, have unveiled a fundamentally new type of optical spectrometer that delivers ...

Abstract: Convolution is fundamental in digital signal processing across many applications. Existing works enable N-point linear convolution via N-point right-angle circular convolution (RCC) based on ...

Abstract: In this paper, we present a relative transfer function (RTF) identification method for speech sources in reverberant environments. The proposed method is based on the convolutive transfer ...

The Fourier Neural Operator (FNO) [1] is a neural operator with an integral kernel parameterized in Fourier space. This allows for an expressive and efficient architecture. Applications of the FNO ...

Our research proves a conjecture from string theory asserting the vanishing of a specific convolution sum arising in the 4-graviton scattering amplitude in 10-dimensional type IIB string theory. The ...

Quantum Fourier analysis is a powerful tool in mathematical physics. Here, we introduce quantum, higher-order Fourier analysis (q-HOFA). We explore some mathematical properties of this theory and show ...

Department of Chemistry, UCL (University College London), 20 Gordon Street, London WC1H 0AJ, U.K. Department of Chemistry, Institute of Environmental Studies and Natural Resources (i-UNAT, FEAM), ...