Generalized sub band analysis and signal synthesis - Evgeny G. Zhilyakov; Sergei P. Belov; Ivan I. Oleinik; Sergei L. Babarinov; Diana I. Trubitsyna (Institute of Advanced Engineering and Science, 2020)
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