Scientific journal
Scientific Review. Technical science
ISSN 2500-0799
ПИ №ФС77-57440

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THE MATRIX APPROACH OF SYNTHESIS OF SYSTEMS OF SIGNALS WITH THE GIVEN PROPERTIES

Gaychuk D.V. 1 Gaychuk V.U. 2
1 Stavropol State Agrarian University
2 North-Caucasus Federal University
In article the method of synthesis of ensembles of the discrete orthogonal signals which cornerstone unitary conversion of the initial system of signals presented in the form of a complex matrix is considered. As in case of unitary conversions the norm of vectors, distances, angles, orthogonality are invariant, realizing conversion it is possible to receive systems of signals with new properties, but saving thus the orthogonality. Results of researches showed that values of side peaks autocorrelated and mutually correlative functions of signals are defined by combinations of the appropriate phase coefficients. And values of side peaks of correlative functions of the transformed system of signals besides depend on the linear combinations of phase parameters of the unitary operator. Thus, purposefully changing parameters of the unitary operator, it is possible to receive systems of the discrete orthogonal signals with the required correlative properties. The task of synthesis is consolidated to searching of joint area of admissible solutions of the linear equations of a look Ах=В.