NEW CLASS OF DIGITAL MALMQUIST-TYPE ORTHOGONAL FILTERS BASED ON THE GENERALIZED INNER PRODUCT; APPLICATION TO THE MODELING DPCM SYSTEM

A new class of cascade digital orthogonal filters of the Malmquist type based on bilinear transformation for mapping poles to zeroes and vice versa is presented in this paper. In a way, it is a generalization of the majority of the classical orthogonal filters and some newly designed filters as well. These filters are orthogonal with respect to the generalized inner product which is actually a generalization of the classical inner product. Outputs of these filters are obtained by using polynomials orthogonal with respect to the new inner product. The main quality of these filters is that they are parametric adaptive. The filter with six sections is practically realized in the Laboratory for Modeling, Simulation and Control Systems. Performances of the designed filter are proved on modeling and identification of the system for differential pulse code modulation. Real response and response from the proposed filter are compared with regard to the chosen criteria function. Also, a comparative analysis of the proposed filter with some existing filters is performed.

Generalized cascade orthogonal filters based on symmetric bilinear transformation with application to modeling of dynamic systems

This paper presents generalized orthogonal cascade filters based on bilinear transformation for mapping poles to zeroes and zeroes to poles in transfer functions. The filters are orthogonal with respect to a new generalized inner product. Actually, they represent a generalization of several classes of existing traditional filters: the ones obtained by using linear transformation of poles to zeroes, and the ones obtained by reciprocal transformation of poles to zeroes. Generalized filters provide obtaining more precise models of dynamic systems. This is verified by comparison between models based on new filters and models based on classical filters. Practical realization of these filters with adjusting parameters of bilinear transformation and transfer function is performed. An application in modeling continuous-time systems as a complex industrial process is given, and it is shown that in that way we obtain more quality models than by using the classical filters.