A synthesis procedure for 90° fan filters

The synthesis of fan filters [1] is approached using a procedure developed by Hirano and Aggarwal [4] and an index transformation given by Chang and Aggarwal [5] which rotates the prototype frequency response . A polynomial factorization reduces the realization algorithm to a series-parallel combination of four one-dimensional all-pass filters. A simplified structure for digital all-pass filters is indicated. An efficient method of approximating zero phase shift is indicated. The associated numerical synthesis procedure consists of evaluating a single equation for a number of arguments. The realization of a fan filter based on an th-order one-dimensional prototype requires multiplications per point.