Two efficient structures for 2D digital filter implementation

Abstract

In the paper, a new efficient structure for two-dimensional digital filters with separable denominator, denoted as 2D ZL, is derived based on a set of special polynomial operators. For a (M, N)th order filter, this structure possesses MN+3(M+N)+1 nontrivial parameters plus M+N free parameters, compared to the optimal state-space realisation which has (M+N+1)2 nontrivial parameters. The equivalent state-space realisation of the 2D ZL yields another interesting efficient structure. Performance analysis is carried out for both structures by deriving the expressions of roundoff noise gain and L2-sensitivity measure. A genetic algorithm is proposed to efficiently solve the optimal structure problems. Two examples are given to show that the optimised proposed structures can yield a better performance than the shift-operator and delta-operator based structures and even outperform the optimal fully parameterised state-space realisation.