The Carathéodory-Fejér method for recursive digital filter design

A new technique for rational digital filter design is presented which is based on results in complex function theory due to Takagi, Krein, and others. Starting from a truncated or windowed impulse response, the method computes the unique optimum rational Chebyshev approximation with a prescribed number of stable poles. Both phase and magnitude are matched. Deleting the noncausal (unstable) part of the Chebyshev approximation yields a stable approximation of specified order (M,N) which is close to optimal in the Chebyshev sense. No iteration is involved except in the determination of an eigenvalue and eigenvector of the Hankel matrix of impulse response coefficients. In this paper the algorithm is specified and practical examples are discussed.