2-D FIR Filter design via semipolynomial approximation

TLDR: A technique is described for the design of general two-dimensional linear-phase FIR filters which yields 2-D filter designs which are not necessarily Chebyshev-optimal, but experience has shown them to be good designs in cases where the optimal solution is known.

Abstract: A technique is described for the design of general two-dimensional linear-phase FIR filters. It is based upon a two-step approach: (i) approximate the ideal frequency response by a semi-polynomial function, i.e., one which is a linear combination of Chebyshev basis functions in one frequency variable; then (ii) approximate this semi-polynomial by the 2-D filter response. This procedure yields 2-D filter designs which are not necessarily Chebyshev-optimal, but experience has shown them to be good designs in cases where the optimal solution is known. Furthermore, the algorithm is computationally fast and thus suited to large filter orders. Filter response specifications need not have particular topographies other than the symmetries implied by linear-phase conditions.