Nonlinearizad of Fast Fourier Transform
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
A unified mathematical form of reversible nonlinear transformations based on a nonlinear tensor product is presented in the form of fast algorithms. The main goal of this article is to show that almost all Fourier transforms (FFTs) can be both generalized and non-linear. Nonlinearity and generalization of the FFT are based on two recursive rules, which generate nonlinear transformations using a fast algorithm. For each rule, simple relations indicate the number of elementary nonlinear operations required by the fast algorithm. The resulting scheme is formed in three stages. The first step involves the so-called 2×2 Basic Non-Linear Transforms (BNLT). The second step is based on sparse nonlinear transformations (SNLTs), which are direct sums of BNLTs. The third step is Fast Nonlinear Transform (FNLT) as an SNLTS overlay product.
Keywords: nonlinear transforms; nonlinear Fourier transforms; fast algorithms.
For citation: Labunets V., Chasovskikh V., Starikov E. Nonlinearizad of fast Fourier transform. Digital models and solutions. 2023. Vol. 2, no. 2. DOI: 10.29141/2782-4934-2023- 2-2-1. EDN: TDVEMG.
