Efficient Design of Two-Dimensional Separable Denominator Digital Filters Using Symmetries

Two-dimensional (2-D) digital filter design requires much computational effort. This paper proposes a technique for reduction of computational effort in 2-D separable denominator digital filter design. The proposed technique exploits diagonal symmetry or anti-symmetry of 2-D impulse response specifications. It is known that a 2-D separable denominator digital filter can be decomposed to the cascade of two 1-D digital filters with 1-input/multi-output and multi-input/1-output, respectively. Such decomposition is called the reduced-dimensional decomposition. In this paper, 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 anti-symmetry. As a result, the computing time in the design procedure is 40–50 percent reduced in comparison with the design method which does not use symmetries.