Fast Spectral Analysis in Vilenkin-Krestenson Function Basis

A synthesis method for the fast Fourier transformation in the Vilenkin-Krestenson basis of generalized functions is considered. The method brings to effective modifications of fast algorithms of the spectrum analysis for various ways of the rarefaction of discrete signal finite samples in both fixed and moving time intervals. Quantitative estimations of the computation complexity of the developed algorithms are given along with specific examples illustrating their operationability and effectiveness.