Geometric algebra integral transforms and their applications

Abstract

Abstract In geometric algebra (GA), real and complex integral transforms (Fourier transforms, linear canonical transforms (LCTs), wavelets, fractional Fourier transforms, special affine Fourier transforms, etc.) can be generalized to holistic higher-dimensional quaternionic, octonionic and Clifford GA versions. This review introduces the foundations of these generalizations, provides representative examples of these new types of transforms and refers to some of their applications in mathematics, physics and engineering. This article is part of the theme issue ‘Modern applications of geometric algebra’.