Generalized sub band analysis and signal synthesis

Evgeny G. Zhilyakov, Sergei P. Belov, Ivan I. Oleinik, Sergei L. Babarinov, Diana I. Trubitsyna


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


Eigen values and vectors; Subband analysis and synthesis fourier transform proportion of the euclidean signal norm; Subband matrices

Full Text:




  • There are currently no refbacks.

Bulletin of EEI Stats