Design of denominator separable 2-D IIR filters

Abstract Optimal design of an important class of two-dimensional (2-D) digital IIR filters from spatial impulse response data is addressed. The denominator of the desired 2-D filter is assumed to be separable into two 1-D factors. The filter coefficients are estimated by minimizing the l 2 -norm of the error between the prescribed and the estimated spatialdomain responses. The denominator and numerator estimation problems are theoretically decoupled into separate problems. The decoupled criteria have reduced dimensionalities. The denominator criterion is simultaneously optimized w.r.t. the coefficients in both dimensions using an iterative algorithm. The numerator coefficients are found in a straightforward manner. If the desired response is known to be symmetric, the proposed algorithm can be constrained to produce optimal denominators which are identical in both domains. The performance of the algorithm is demonstrated with simulation examples.