Abstract: The fractional Fourier transform (FRFT), which is a generalization of the Fourier transform (FT), has emerged as a very efficient mathematical tool for signals which are having ...

Convolution is a remarkable property of the Fourier transform, often cited in the literature as the “faltung theorem”. Convolution is a remarkable property of the Fourier transform, often cited in the ...

Title: Integers and Delta Functions: Convolution Isomorphism, Fourier Duality, and the Poisson Summation Formula (Revised Edition with Supplements) Note: This manuscript is a mathematically and ...

TL;DR: We show how the relation of convolution, circulant matrices and the Fourier transform generalizes to the quaternionic domain. A Lipschitz constant bounding application acts as a ...

A mathematical theorem stating that a PERIODIC function f(x) which is reasonably continuous may be expressed as the sum of a series of sine or cosine terms (called the Fourier series), each of which ...