Abstract

In order to design 2-D digital systems with variable characteristics, product-separable IIR filters with feedbacks in each dimension are studied. The stability and response of such systems with different situations are analyzed and discussed. Belonging to one of the methods of generation of VSHP in z-domain, product-separable IIR filters with dimensional feedbacks offer variable characteristics. The variable feedback gain in one-dimension is analyzed with all the other coefficients based on Schussler's Theorem. The stable conditions for the feedback in terms of other coefficients are obtained and hence a stable range of the feedback gain is determined. Within the stable range of feedback in each dimension, different filters' 2-D frequency responses have been studied and observed with different situations. Significant variable characteristics and different 2-D symmetries are shown with stable responses. Relations between the feedback and response are discussed. Furthermore, to extend this analysis to higher order systems, a computerized analysis method and algorithm is proposed and implemented. This approximation method can work with any order of IIR or FIR filters and has low computation complexity. More complex systems with variable characteristics can be composed and examples of Image Processing with these filters are simulated as space-domain applications.