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.

Mathematics is often seen as perfect—consistent, complete, and immune to contradiction. But in the early 20th century, a breakthrough proved that no mathematical system can ever explain everything ...

Large language models (LLMs) have astounded the world with their capabilities, yet they remain plagued by unpredictability and hallucinations – confidently outputting incorrect information. In ...

ABSTRACT: The quaternion linear canonical transform (QLCT) is defined in this paper, with proofs given for its reversibility property, its linear property, its odd-even invariant property and ...

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 ...

Convolution is used in a variety of signal-processing applications, including time-domain-waveform filtering. In a recent series on the inverse fast Fourier transform (FFT), we concluded with a ...

Event-based cameras are bio-inspired vision sensors that mimic the sparse and asynchronous activation of the animal retina, offering advantages such as low latency and low computational load in ...

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 ...

Could monkeys randomly striking keys on a keyboard for an for an infinite period of time produce a Shakespearean work? Doubtful, says a new study of the "Infinite Monkey Theorem." On more certitude in ...

It turns out a monkey – given an infinite amount of time and a typewriter – wouldn't be able to write Shakespeare before the universe ends, according to a new study. HARRY SHEARER: (As Charles ...

Two teenagers found ten new proofs of the Pythagorean theorem using trigonometry, debunking a century-old belief. Calcea Johnson and Ne’Kiya Jackson were St. Mary’s Academy students in New Orleans and ...