An DFII based structure for 2-D separable-denominator digital filters with very low L2-sensitivity measure

In this paper, a new 2D digital filter structure is derived based on a more generalized polynomial operator. This new structure is a mixture of direct-form II (DFII) and direct-form II transposed (DFTIIt) structures. The coefficient sensitivity is analyzed using a pure L₂-norm subject to L₂-scaling constraints for the new structure and its equivalent state-space realization, both of which are every sparse and can be optimized with the degrees of freedom. An numerical example is given to illustrate that the optimized proposed structures can have a very low sensitivity measure.