Windowed Octonionic Fourier Transform

In this article, we introduce the concept of the windowed octonion Fourier transform (WOFT) by taking the octonion-valued function as the window function on the space of square integrable octonion-valued functions on R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^3$$\end{document}. Some properties of the windowed octonion Fourier transform (WOFT) like left linearity, parity, specific shift, inversion, orthogonality and Hausdorff–Young inequality were also established. Towards the culmination of this paper, we establish the Pitt’s inequality and hence some uncertainty principle for the proposed transform. Some potential applications were also added to show the effectiveness of this paper.