Application of power-spectrum estimation in the Vilenkin-Christenson-Functions (VCF) basis for finding the weighting vector of an M-ary filter

Abstract

The properties of M-ary correlation matrices of interferences and of their spectra have been considered. It has been shown that such matrices have systems of eigenvectors coinciding with the discrete-Fourier-transform matrices in the corresponding ZCF bases. This allowed an algorithm to be obtained for the functioning of a tunable filter, which is convenient for digital implementation. The proposed algorithm has been compared with the classical "sliding-window" method in terms of the number of arithmetic operations required for its implementation.