Using of the matrix representation of algorithms of the fast Fourier and Hartley transforms in the problems of “sliding” spectrum analysis

Abstract

Matrix formulae for calculating of the fast Fourier and Hartley transforms for a sequence of radar signal readings are obtained. The formulae obtained allow us to implement the “sliding” (or galloping”) spectrum analysis with rational using of information about the spectrum of a previous step for each new position of a time window. The matrix formulae of the Hartley transforms with an arbitrary base are obtained. These formulae are a generalization of the well-known Hartley formula for splitting of the initial sequence into the two sequences, namely, with the even and odd numbers.