An efficient approach for the synthesis of 2-D recursive fan filters using 1-D prototypes

An elliptic approximation-based design approach is proposed for obtaining 2-D recursive fan filters. The 1-D elliptic filter is reduced to a cascade-parallel combination of all-pass sections and is then used as a prototype for fan filter synthesis, resulting in final realization of 2-D transfer functions using allpass filters. It is shown that the synthesis procedure not only gives a filter that has far fewer coefficients but also enjoys a very low computational complexity