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Diana I. Trubitsyna
Belgorod State National Research University
Electrical & Electronics Engineering

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Generalized sub band analysis and signal synthesis Evgeny G. Zhilyakov; Sergei P. Belov; Ivan I. Oleinik; Sergei L. Babarinov; Diana I. Trubitsyna
Bulletin of Electrical Engineering and Informatics Vol 9, No 3: June 2020
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (453.703 KB) | DOI: 10.11591/eei.v9i3.1709

Abstract

Currently, one of the main approaches used in analyzing properties and synthesis of signals in various classes is the subband methodology, which is carried out from the position of Fourier transform of signal samples (frequency representations) into subbands of the transform definition domain  (transformants). In this case, the main tool, which is widely used for subband analysis (including wavelet analysis), is usage of bandpass filters (mainly those with finite impulse response or FIR filters). The present paper  introduces the basics of building a theory forsubband analysis / signal  synthesis for various classes, and using transformations based on any  orthonormal basis with weight. This proposed approach is based on the  concept of Euclidean signal norm square fraction in a given subband of the transformant definition domain. It is shown that the basis for mathematical apparatus of subband analysis is a new class of matrices, called subband ones. Some eigenvalue properties of these matrices are established, and the problem of optimal selection for additive signal components is formulated and solved
Co-Authors Evgeny G. Zhilyakov Ivan I. Oleinik Sergei L. Babarinov Sergei P. Belov