Design of complex coefficient variable fractional-delay allpass digital filters by eigenfilter approach

In this paper, the technique of eigenfilter approach is applied to the design of complex coefficient variable fractional-delay (VFD) allpass digital filters. The objective error function is formulated into a quadratic form a^TQa where a is a coefficient vector and Q is a real, symmetric and positive-definite matrix. By Rayleigh principle, the eigenvector corresponding to the smallest eigenvalue of Q minimizes the error function, and is the desired solution. Several examples are presented to demonstrate the effectiveness of the proposed method.