On a new class of quasi-orthogonal filters

In this article, a new class of quasi-orthogonal filters, based on the Legendre and Malmquist-type quasi-orthogonal polynomials, is presented. These filters are generators of quasi-orthogonal functions for which we derive and present all important properties and relations. Our article is based on the classical theory of orthogonality and orthogonal functions, and also on new results in this field of mathematics. Based on theoretical results, we design schemes for the realisation of these filters. Finally, a trail quasi-orthogonal filter is practically realised and its quasi-orthogonality is proven by performing experiments. Quasi-orthogonal filters can be successfully used for signal approximation as well as for modelling, identification, analysis, synthesis and simulation of dynamical systems.