Spatial-domain design of two-dimensional recursive digital filters

An optimization technique is proposed to design stable two-dimensional recursive digital filters with prescribed impulse or step response. The performance measure used is the weighted ℓp-norm of the error function. The optimization is carried out using the Davidon-Fletcher and Powell algorithm. Throughout the paper, the local state space model is used to represent the filter. The matrix derivative linear operator is used to calculate the performance measure gradient vector. A design for an asymmetric-half-plane filter is solved to illustrate the proposed technique.