New many-parameter Fourier–Clifford transforms
Valery G. Labunets - Doctor of Technical Sciences, Professor of Chess Art and Computer Mathematics Dept. Ural State University of Economics
Viktor P. Chasovskikh - Doctor of Technical Sciences, Professor of Chess Art and Computer Mathematics Dept. Ural State University of Economics
Evgeny N. Starikov - Candidate of Economic Sciences, Associate Professor, Acting Head of Chess Art and Computer Mathematics Dept. Ural State University of Economics
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.
For citation: Labunets V. G., Chasovskikh V. P., Starikov E. V. New many-parameter Fourier–Clifford transforms. Digital models and solutions. 2023. Vol. 2, no. 3. Pp. 5–22. DOI: 10.29141/2949-477X-2023-2-3-1. EDN: MLQGCK.
