Optimal minimax two-dimensional FIR design using a multiple simplex exchange

A new algorithm is presented for the design of two-dimensional linear phase FIR filters that best approximate an arbitrary magnitude response in the Chebyshev sense. The algorithm is an extension of one proposed recently by the authors (see Proc. IEEE ICASSP, vol. 3, 1993) for the design of one dimensional filters. It consists of an iterative sequence of linear programs solved by a variation of the simplex algorithm. Convergence is stable. The true optimal design is found, to within an arbitrarily small error tolerance, in contrast with several of the recently published approximate techniques. Sparse and/or non-causal impulse coefficient designs can be done in a straightforward manner. Examples are given demonstrating the performance of this new algorithm over previously published techniques with respect to speed, stability of convergence, and accuracy. The new method has been used to design filters larger than can be accommodated by other methods known to the authors. A 41×41 design example is given