Generalized sub band analysis and signal synthesis

Abstract

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