A structured matrix approach for spatial-domain approximation of2-D IIR filters

摘要

This work addresses least-squares (LS) approximation of anprescribed spatial response by a quarter-plane 2-D IIR filter. Usingnstructured matrix representation it is shown that the spatial domainnerror vector between the desired and estimated responses is linearlynrelated to the numerator coefficients and nonlinearly related to thendenominator coefficients. The numerator and denominator estimationnproblems are theoretically decoupled without affecting the optimalitynproperties. The decoupled denominator criterion possesses anquasi-quadratic form and its optimization is computationally efficientnrequiring very few iterations, The numerator is estimated linearly in ansingle step. Effectiveness of the algorithm is demonstrated with severalnexamples