Introduction

This chapter surveys the historical development of quaternion and Clifford Fourier transforms and wavelets. Fundamental is the generalization of integral transforms from real and complex numbers to quaternions and Clifford's geometric algebras of quadratic spaces. The development of these hypercomplex Fourier transforms and wavelets has taken place in several different threads, reflected in the overview of the subject presented in this chapter. First an overview of the development of quaternion Fourier transforms (QFT) is presented, and second, the development of Clifford Fourier transforms (CFT). Thirdly, since wavelets are a more recent development, and the distinction between their quaternion and Clifford algebra approach has been much less pronounced than in the case of Fourier transforms, the history of both quaternion and Clifford wavelets is also reviewed. [125 words]