Open AccessNew application of non-binary Galois fields Fourier transform: digital analog of convolution theorem
Author(s) -
Elizaveta S. Vitulyova,
Dinara K. Matrassulova,
И. Э. Сулейменов
Publication year - 2021
Publication title -
indonesian journal of electrical engineering and computer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.241
H-Index - 17
eISSN - 2502-4760
pISSN - 2502-4752
DOI - 10.11591/ijeecs.v23.i3.pp1718-1726
Subject(s) - convolution (computer science) , mathematics , convolution theorem , transfer function , analog signal , fourier transform , circular convolution , galois theory , discrete mathematics , algebra over a field , pure mathematics , mathematical analysis , computer science , digital signal processing , fractional fourier transform , fourier analysis , artificial neural network , artificial intelligence , computer hardware , electrical engineering , engineering
It is shown that the use of the representation of digital signals varying in the restricted amplitude range through elements of Galois fields and the Galois field Fourier transform makes it possible to obtain an analogue of the convolution theorem. It is shown that the theorem makes it possible to analyze digital linear systems in same way that is used to analyze linear systems described by functions that take real or complex values (analog signals). In particular, it is possibile to construct a digital analogue of the transfer function for any linear system that has the property of invariance with respect to the time shift. It is shown that the result obtained has a fairly wide application, in particular, it is of interest for systems in which signal processing methods are combined with the use of neural networks.