Generalized sub band analysis and signal synthesis

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

Экспериментальные Исследования По Распознаванию Малоразмерных Объектов На Видеоизображениях При Использовании Многомерных Пространственно-Субполосных Векторов

“…Применение субполосного представления видеоизображений позволяет сохранять как пространственную, так и частотную структуру изображения объекта [Zhilyakov, Belov, Oleinik, Babarinov, Trubitsyna, 2020]. Это может дать преимущество перед другими методами, использующими правила распознавания с предварительным определением и использованием параметров информативности признаков распознавания.…”

Experimental studies of differences in the distribution parameters of multidimensional spatial-subband object vectors on video images during subband information processing

“…Application of sub-band representation of video images allows saving both spatial and frequency structure of the object image [4,5]. This can give an advantage over other methods that use recognition rules with preliminary determination and use of parameters of informativity of recognition signs.…”