General Steerable Two-sided Clifford Fourier Transform, Convolution and Mustard Convolution

In this paper we use the general steerable two-sided Clifford Fourier transform (CFT), and relate the classical convolution of Clifford algebra-valued signals over Rp,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^{p,q}}$$\end{document} with the (equally steerable) Mustard convolution. A Mustard convolution can be expressed in the spectral domain as the point wise product of the CFTs of the factor functions. In full generality we express the classical convolution of Clifford algebra signals in terms of finite linear combinations of Mustard convolutions, and vice versa the Mustard convolution of Clifford algebra signals in terms of finite linear combinations of classical convolutions.