Reduction of the number of parameters in the design of 2-D digital filters

In the filter design, an easy way of reducing the number of parameters is to choose the filter structure to be more restrictive at the expense of its accuracy to some extent. This paper deals with the design of two-dimensional separable-denominator recursive digital filters using a canonic local state-space model. Under the assumption that the filter order, i.e., the denominator order is fixed, the reduction of the total number of parameters is accomplished by adjusting the numerator order. A canonic form is used to avoid the mutual interference among parameters and to reduce the amount of calculations in the design technique using a local state-space model. A straightforward algorithm is developed via the Cayley-Hamilton theorem to find the suboptimal model which approximates a desired impulse response in some sense. This provides the initial estimate to minimize a performance index in the design and it is very crucial in order to attain a good convergence in the nonlinear optimization problem. The iteration is performed by any suitable nonlinear optimization method.