Design techniques for two-dimensional digital filters

The theory for designing finite-duration impulse response (FIR) digital filters can readily be extended to two or more dimensions. Using linear programming techniques, both frequency sampling and optimal (in the sense of Chebyshev approximation over closed compact sets) two-dimensional filters have been successfully designed. Computational considerations have limited the filter impulse response durations (in samples) to 25 by 25 in the frequency sampling case, and to 9 by 9 in the optimal design case. However, within these restrictions, a large number of filters have been investigated. Several of the issues involved in designing two-dimensional digital filters are discussed.