Method for Structuring the Fourier Discrete Cosine Transform in the Modular Arithmetic of the Haar–Krestenson Number-Theoretic Basis

A theory and a solution are presented to the applied problem of structuring the Fourier discrete spectral cosine transform (FDSCT) in the modular arithmetic of the Haar–Krestenson number-theoretic basis. A high-performance algorithm for FDSCT was developed by adapting the orthogonal functions of the Fourier, Rademacher, Krestenson, and Haar bases to the asymptotic autocovariance of the signals being investigated. A method for structuring the FDSCT algorithm in the modular arithmetic of the residue number system of the Haar–Krestenson number-theoretic basis was implemented. The structure of an implementation of a special FDSCT processor and its microelectronic basic components are given.