UDC 004.932
ORTHOGONAL TRANSFORMATIONS BASED ON LINEAR SEQUENCES OF MAXIMUM LENGTH
E. A. Trushina, senior lecturer, department of electronic computers, RSREU, Ryazan, Russia;
orcid.org/0000-0001-6019-225X, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
N. N. Grinchenko, doctor of technical sciences, associate professor, department of electronic computers,
RSREU, Ryazan, Russia;
orcid.org/0000-0003-2318-276X, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
B. V. Kostrov, doctor of technical sciences, professor, head of the department of electronic computers,
RSREU, Ryazan, Russia;
orcid.org/0000-0002-2984-4480, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
This article considers the problem of proving the orthogonality of a system of functions formed from cyclic
shifts of m-sequences. The relevance of this study stems from the importance of the properties of orthogonal
systems in the fields of coding and signal processing. The aim of this work is to formally prove the orthogonality of the specified system of functions, based on the properties of m-sequences and their correlation characteristics. The main objectives are: analyzing the properties of m-sequences, constructing a matrix with elements from the ±1 alphabet, proving its orthogonality based on the properties of the cyclic shift of sequences of maximum period; formulating the assertion with subsequent justification. The orthogonality
properties of the constructed system are proven, confirming its suitability for application in various areas of
digital technology and information theory. The results of transformations using an orthogonal basis based
on an m-sequence are presented.
Key words: orthogonal function system, maximum length m-sequence, orthogonal transformations, image
processing.