Optimal design of 2-D IIR filters-strictly proper case

The problem of optimal design of a class of two-dimensional (2-D) digital infinite impulse response (IIR) filters from spatial impulse response data is addressed. The denominator of the desired strictly proper 2-D filter is assumed to be separable. The filter coefficients are iteratively estimated by maintaining the t₂-norm of the error between the prescribed and the estimated spatial domain responses. The complete subspace orthogonal to the 2-D model fitting error is identified. It is shown that by appropriate choice of the orthogonal subspace, the exact fitting error criterion can be simultaneously optimized with respect to the coefficients in both dimensions. If the desired response is known to be symmetric, the proposed algorithm will produce optimal denominators which are identical in both domains. The performance of the algorithm is demonstrated with some simulation studies