2023/06/08 by Manish Kumar, Kumar, Manish, Bhawna
Mathematics · Physics and Astronomy · #46F12 #53D22 #Advanced Differential Geometry Research #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2306.06127
openalex publication_date 2023/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The uncertainty principle is a fundamental principle in theoretical physics, such as quantum mechanics and classical mechanics. It plays a prime role in signal processing, including optics, where a signal is to be analyzed simultaneously in both domains; for instance, in harmonic analysis, both time and frequency domains, and in quantum mechanics, both time and momentum. On the other hand, many mathematicians, physicists, and other related domain researchers have paid more attention to the octonion-related integral transforms in recent years. In this paper, we define important properties of the windowed octonion linear canonical transform (WOCLCT), such as inversion, linearity, parity, shifting, and the relationship between OCLCT and WOCLCT. Further, we derived sharp Pitt's and sharp Young-Hausdorff inequalities for 3D WOCLCT. We obtain the logarithmic uncertainty principle for the 3D WOCLCT. Furthermore, Heisenberg's and Donoho-Stark's uncertainty principles are derived for WOCLCT, and the potential applications of WOCLCT are also discussed.