Synthesis of symmetrical functions of golden ratio

Authors

  • Анатолий Яковлевич Белецкий National Aviation University
  • Владимир Андреевич Лужецкий Vinnytsia National Technical University

DOI:

https://doi.org/10.18372/2410-7840.18.11090

Keywords:

the system of Walsh functions, matrix indicator Walsh systems, Kronecker multiplication, the golden proportion, Walsh-like system of the golden ratio functions

Abstract

The article deals with the formation of symmetric Walsh-like systems functions of the golden ratio (FGR) binary-power order. The basis of the construction of systems FGR on the method of Kronecker product, which is used in the synthesis of the Walsh-Kronecker systems. Generating matrix for the Walsh-Kronecker systems is the Hadamard matrix of the second order, in which the element is substituted with an element -1 on -α, equal to the ratio of the golden ratio. Algorithms direct preparation systems FGR arbitrary binary-power order, similar to the Walsh-Hadamard and Walsh-Paley. Synthesis of the full set of symmetrical systems FGR carried permutation of basic functions systems, the Walsh-Paley. Rules permutation function sets the indicator matrix of the corresponding systems. Nondegenerate indicator is symmetrical with respect to the field of auxiliary diagonal (0,1) matrix, where in the weight of each column (as rows) of the matrix, equal to the sum of ones, must be an odd number.

Author Biographies

Анатолий Яковлевич Белецкий, National Aviation University

Doctor of Science, Professor, Honored Scientist of Ukraine, Laureate of the State Prize of Ukraine in Science and Technology, Professor of Department Electronics of National Aviation University

Владимир Андреевич Лужецкий, Vinnytsia National Technical University

Doctor of Science, Professor, Head of Information Security Academic Department, Vinnytsia National Technical University

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Published

2016-12-12

Issue

Vol. 18 No. 4 (2016)

Section

Articles

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