Razvoj nove klase ortogonalnih filtara s primenom u modeliranju, analizi i sintezi sistema za diferencijalnu impulsno kodnu modulaciju

Abstract

This PhD dissertation deals with development of new classes of orthogonal filters based on symmetric transformation of their poles to zeroes and vice versa. The filters based on reciprocal transformation are developed and the generalized Malmquist filters orthogonal with respect to a special inner product are designed in this way. The orthogonal filters by using bilinear transformation, including several classes of classical orthogonal cascade filters (Legendre, Laguerre, Müntz-Legendre, Malmquist), are also designed. These filters are practically realized both in analogue and digital techniques. The main quality of these filters is a possibility of adaptive adjustment of filter parameters, i.e. parameters of bilinear transformation, achieving the best filter performances. The final result of this part of research is a wide range of applications of these filters in identification, modelling, analysis, and design of technical systems. The analogue versions of filters are applied in modelling of the system for rubber strip cooling in tyre industry, and their digital versions in modelling of telecommunication system for differential pulse code modulation (DPCM system). It is verified that the models obtained by using these new filters are of higher quality than the models based on classical filters. The other part of research in PhD dissertation refers to the mentioned DPCM system. A complete analysis of DPCM system with arbitrary order predictor is performed for the first time. This relates to the consideration of stability by classical approach, as well as to stochastic stability analysis. The analysis of robust stability by using Kharitonov method is also performed for both deterministic and stochastic case, as well as for low- and high orders of predictors. The parametric sensitivity related to different order-predictors coefficients is also analyzed.