History of quaternion and Clifford-fourier transforms and wavelets

The development of hypercomplex Fourier transforms and wavelets has taken place in several different threads, reflected in the overview of the subject presented in this chapter. We present in Section 1 an overview of the development of quaternion Fourier transforms, then in Section 2 the development of Clifford Fourier transforms. Finally, since wavelets are a more recent development, and the distinction between their quaternion and Cliord algebra approach has been much less pronounced than in the case of Fourier transforms, Section 3 reviews the history of both quaternion and Clifford wavelets