New many-parameter Fourier–Clifford transforms

Abstract

The article shows how ordinary complex-valued Fourier transforms are extended to Cliffordean-valued many-parameter Fourier transforms (MPFCTs). Each MPFCT depends on finite set of independent parameters (angles), which could be changed independently one from another. When parameters are changed, MPFCT is also changed taking form of a set of known and unknown orthogonal transforms. Development of MPFCTs includes operator exponential representations, based on all parameterized imaginary units’ square roots of minus one in Clifford algebra.

Keywords

• fourier–clifford transforms
• many-parameter transforms
• fast algorithms