Efficient design of two-dimensional separable denominator digital filters using symmetries

The authors propose a technique for reduction of computational effort in 2-D separable-denominator digital filter design. The technique exploits diagonal symmetry or antisymmetry of 2-D impulse response specifications. It is known that a 2-D separable-denominator digital filter can be decomposed into a cascade of two 1-D digital filters with 1-input/multi-output and multi-input/1-output, respectively. Such a decomposition is called the reduced-dimensional decomposition. It is shown that the design problems of two 1-D digital filters can be reduced to the design problem of a single 1-D digital filter by exploiting diagonal symmetry or antisymmetry. As a result, the computing time in the proposed design procedure is 40-50% shorter than in a design method that does not use symmetries