Alternances of Fourier spectra for sequences of Hadamard matrix families

The aim of the work is to improve the algorithms for searching for orthogonal sequences of cyclic blocks of Hadamard matrices H^TH = nI, n is size, I is the identity matrix, and matrices of odd and even orders K^TK = ωI, where ω ≤ 1, which have properties similar to Hadamard matrices – a small values of elements (levels), both integer and irrational. The content of the problem of this search is that when cross-comparing even a small number of the sequence for orthogonality, the volume of comparisons grows as square of this number. Methods for accelerating the solution are associated with the selection of individual features, filtering by which weed out more than 99 % of the primary material before cross-comparison. Threshold restrictions on the Fourier spectra of sequences have such properties. The result of the work is an indication of the conditions under which the threshold is observed automatically due to the alternance of the spectral dependences in the vicinity of the half value of the filter threshold (previously, only the threshold was indicated). In the conclusion of the article, the area of application of the desired sequences is noted – the processing and masking of video information by orthogonal matrices, for which the marked acceleration is significant and allows you to build new video systems.

Authors: N. A. Balonin, D. V. Kurtyanik

Direction: Informatics, Computer Technologies And Control

Keywords: Hadamard matrices, orthogonal sequences, Fourier filters, alternances

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