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Telecommunications and Radio Engineering
SJR: 0.202 SNIP: 0.2 CiteScore™: 0.23

ISSN Imprimer: 0040-2508
ISSN En ligne: 1943-6009

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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v56.i3.20
11 pages

Matrix Algorithms of Accelerated Computation of Fast Fourier Transform and Fast Hartley Transform

S. L. Zlobin
A. Ya. Stal'noy

RÉSUMÉ

The conception of "running" or "sliding" spectrum is frequently used in spectral analysis and digital signal processing. "Running" or "sliding" spectral analysis is used in digital matched filtering of reflected signal in radiolocation, in adaptive arrays, in adaptive digital filtering, in speech signal and biomedical signal processing. Besides, operation of "running" spectral analysis can be implemented not only via Fourier transform, but on the basis of recently proposed Hartley transform too. Usually, in practice, fast transform algorithms are employed: FFT or FHT. A new matrix algorithm of accelerated computation of "running" ("sliding") Fourier or Hartley spectrum is described in the article. Spectrum length is arbitrary and equal to N, where N = bs, b is the FFT or FHT algorithm radix. Application of the arithmetical apparatus of block matrices and definition of "partial" spectra made it possible to describe "sliding" spectrum accelerated computation process in matrix form. The obtained algorithm is clear, distinct for regularity and simplicity of calculation process, makes it possible to get considerable computation economy in comparison with the common method. The algorithm is written in simple matrix expressions and can be simply programmed.


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