DFII based structures for 2-D separable-numerator digital filters with minimal roundoff noise gain

Presently, most two-dimensional (2-D) digital filters adopt the shift operator. In this paper, a new operator called the ρ-operator is derived for 2-D digital filters and consequently, a new structure is obtained. This structure, which is a mixture of direct-form II (DFII) and direct-form II transposed (DFIIt) structures, is very efficient and provides more degrees of freedom for minimizing the roundoff noise gain of the structure without increasing the computation complexity. A numerical example is given to illustrate the design procedure, which shows that the optimized structure can yield a better performance than the shift and delta operator and even beat the optimal fully parametrized realization.