Abstract

A design of two-dimensional (2D) digital filter with monotonic amplitude-frequency responses using Darlington-type gyrator networks by the application of Generalized Bilinear Transformation is discussed. The proposed design provides the stable monotonic amplitude-frequency responses and the desired cutoff frequency of the 2D digital filters. This 2D recursive digital filter design includes 2D digital low-pass, high-pass, band-pass and band-elimination filters. The proposed design shows that the impedances of doubly terminated RLC networks are integrated into the Darlington-type gyrator networks and the coefficients of the resultant 2D analog transfer functions are function of gyrator constant ( g ). The behavior of the filter is changed not only for the values of resistance, capacitance and inductance of the filter, but also for the value and sign of g. The proposed design uses the Generalized Bilinear Transformation to obtain the digital filter and it provides six parameters to regulate in order to design the desired digital filters. The several constraints are obtained for the monotonic amplitude-frequency responses of the filters. The ranges of g of the each type filter are defined for attaining the monotonic characteristics of the digital filter, because the g has control on the frequency response of the filter. A digital filter transformation method is proposed and the digital filters are transformed by regulating the value or sign of g. A new realization of 2D digital polynomial is given, which is suitable to implement any 2D polynomial with finite order. The performances of the designed 2D digital filters in the image processing applications are discussed and significant improvements in the reconstructed images are obtained by the filters.