Design of 2-D separable in denominator filters using canonic local state-space models

This paper treats the problem of designing two-dimensional (2-D) recursive digital filters using a canonic local state-space model which is separable in the denominator. The use of a canonic form is to reduce the amount of calculations in the state-space design to some extent. A straightforward technique is developed via the Cayley-Hamilton theorem to find the suboptimal model approximating a desired impulse response in some sense. This provides the initial estimate to iteratively minimize a performance index and it is very crucial in order to attain a good convergent accuracy in the nonlinear optimization problem. A mapping from an asymmetric half-plane to a subset of the first quadrant is also proposed to adjust the order of numerator and to design a wider class of 2-D filters. Two examples are presented to illustrate the utility of the proposed technique.