Design of generalised orthogonal filters: application to the modelling of dynamical systems

Abstract

In this article, we define a new class of orthogonal filters with complex poles and zeroes inside their transfer function. This further improvement of classical orthogonal filters allows the possibility to model a wider range of real systems, that is, the systems whose mathematical models have complex zeroes besides real ones. These filters can be applied in the following areas: circuit theory, telecommunications, signal processing, bond graphs, theory approximations and control system theory. First, we describe the rational functions with complex poles and zeroes, and prove their orthogonality. Based on these functions, we designed the block diagram of orthogonal Legendre-type filter with complex poles and zeroes. After that an appropriate analogue scheme of this filter for practical realisation is derived. To validate theoretical results, we performed an experiment with a cascade-connected system designed and practically realised in our laboratories. The experiments proved the quality of the designed orthogonal model in terms of accuracy and simplicity.