Circuit and State-Space Realization of 2-D Allpass Digital Filters via the Bilinear Transform

In this paper the problem of the circuit and state-space realization of first- and second-order two-dimensional (2-D) allpass digital filters is considered. The method uses the 2-D bilinear transform. The multipliers and delay elements required for the realization equals the maximum number of the numerator or denominator coefficients of the given filter. The matrices A,b, and c' and the scalar d of the Givone-Roesser state space model are derived, based on the circuit realization, for first- and second-order allpass digital filters.