Abstract: The linear canonical transform (LCT) plays an important role in many fields of optics and signal processing. Many properties for this transform are already known, however, the convolution ...

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 ...

In the fall of 1915, the foundations of physics began to crack. Einstein’s new theory of gravity seemed to imply that it should be possible to create and destroy energy, a result that threatened to ...

In 2022, two high school students created a trigonometric proof of the Pythagorean Theorem—something that’s only ever been accomplished by a few professional mathematicians. Now, a new article not ...

Two students who discovered a seemingly impossible proof to the Pythagorean theorem in 2022 have wowed the math community again with nine completely new solutions to the problem. While still in high ...

Abstract: In this paper, we present a novel convolution theorem which encompasses the well known convolution theorem in (graph) signal processing as well as the one related to time-varying filters.

Pythagoras Theorem: This article explains the concept of Pythagoras Theorem and its converse. Know the definition, formula, proof, examples and applications of Pythagoras Theorem. Pythagoras Theorem: ...

This is my coursework project for 2023 autumn semester at BSUIR. The project is to study the differences in speed of large convolutions with and without Fourier transform (based on the convolution ...

You might be surprised to learn that you can’t comb the hairs flat on a coconut without creating a cowlick. Perhaps even more surprising, this silly claim with an even sillier name, the “hairy ball ...