Design of smallest size two-dimensional linear-phase FIR filters with magnitude error constraint

This paper presents an online procedure that produces the smallest feasible size of two-dimensional FIR filters with prescribed magnitude error constraint. The procedure uses the mean square normalized error of constrained and unconstrained least-square filters to produce the initial and the subsequent sizes that converge to the smallest feasible one in a few iterations, where the constrained least-square filters are defined as the least-square filters satisfying the magnitude error constraint. The procedure finally returns a smallest size filter that satisfies the magnitude error constraint and has least total squared magnitude error. Design examples of diamond-shaped, rectangular, and elliptic filters are provided, and comparisons with an exhaustive search are given.