Decomposition of FIR digital filters for realization via the cascade connection of subfilters

A method is presented for decomposing even-order linear-phase FIR filters with distinct roots into the cascade connection of second-and fourth-order subfilters. The technique consists of of finding roots of the z-domain filter transfer function by searching a finite region in the complex z plane. Due to symmetry in the impulse response, only the perimeter (the real axis and boundary) and interior of the upper half of the unit circle need to be searched for real and complex values of roots from which the impulse response coefficients of the corresponding subfilters can be directly determined. The root-finding algorithm tests for existence of a root at each interval in a finite grid and then utilizes the Newton-Raphson method to refine the final estimate of each root value. In the two-dimensional (2-D) search, the Cauchy-Riemann relations are exploited to reduce computations and speed convergence. This method has been tested on FIR filters with orders ranging to over 120 and has proven effective in decomposing filters to the cascade realization with identical frequency response characteristics. An example is presented that illustrates the use of this technique.