Complex matrix inversion algorithm for calculating digital system frequency response

Given a signal flow graph for a digital system, one can read the matrix state equation and auxiliary equations needed to find outputs. Phasors are introduced by letting
z = \exp(jw)
where φ < w < 2π. Solution to the resulting matrix equation is based on a method by Froberg. The algorithm is illustrated by computing the response of a 5th order Butterworth frequency spectrum dividing network given in direct form. BASIC code is given which uses MAT statements. A cascade implementation of the low-pass filter is calculated by the same basic algorithm. Results agree with traditional transfer function evaluations on the same computing equipment.