Peculiarities and distinctions between matrix algorithms for fast Fourier and Hartley transforms in the "running" spectral analysis problems

Abstract

The paper describes the unified matrix approach to FFT algorithms, described in [1], for synthesis of algorithms permitting to realize the operation of “running” (or “jumping”) spectral analysis. Here we maximally use information about the spectrum of the preceding step for each new position of the time window. A formula is derived for calculation of Hartley’s transform for a sequence of data expressed in matrix form. The formula represents an extension, to an arbitrary base, of the known Hartley formula using the partition of the initial sequence in two ones—with odd and even numbers.