A design method for complementary recursive fan filters

A very efficient method for designing two-dimensional (2-D) recursive fan filters is presented. The odd-ordered analog elliptical filter is used as a 1-D prototype to synthesize the complementary quadrant fan filters, as well as 90° fan filters, by means of an index transformation. The algorithm results in a great reduction in the required multiplications and in the simplified realization structure composed of all-pass filters as compared with the published design procedures. The design of zero-phase fan filters is also discussed. Only N-1 and 2(N-1) multiplications are needed to implement non-zero- and zero-phase complementary fan filters, respectively, if an Nth-order 1-D prototype elliptical filter is adopted