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Identification of the rational function of multi-dimensional filters and the synthesis of digital two-dimensional inverse and quasi-inverse filters

Krawczyszyn G.

Poznan University of Technology Academic Journals. Electrical Engineering

2007

No 53

7-16

The paper aims at presenting the determination method of coefficients of the rational function of multi-dimensiona! filters K-D in the domain of discrete time on the basis of samples of an impulse response. The transmittance is the quotient of two finite multinominals. Interesting solutions can be obtained in the domain of time, in which samples of an approximated signal are used in the algorithm of selection of coefficients for the multi-dimensional filter N-D. The transformation (h→ a) is applied on the basis of such samples, which yields the rational function W(z), which, in turn, is the transmittance of the filter being analysed. Furthermore, the paper also aims to developing a theory concerning digital two-dimensional inverse and quasi-inverse filters. The quasi-inverse filters obtained by way of optimisation permit to select the approximation degree of a resultant system resulting from a cascade connection of a distortion system and a corrective filter. The paper contains formulae, which permit to design a stable quasi-inverse two-dimensional filter on the basis of the existing mathematical model in the form of the transmittance H(z) of a corrected system or its impulse response. The advantage of the formulae is the possibility to select an approximation degree in relation to the ideal inverse filler or the degree of stabilisation.