Novel approach to high-accuracy all-pass variable-delay filter design

This paper formulates a novel approach to the high-accuracy design of recursive all-pass variable-delay digital filters in the minimax sense by employing the rotated-cone (Rcone) programming. We first show that the variable-frequency-response (VFR) error can be approximated as a rational function with both numerator and denominator expressed as linear functions of the filter coefficients. For simplicity, we call such a rational error function bi-linear error function. Then, we formulate a minimax design as an Rcone-programming problem by means of the bi-linear error function. Since Rcone-programming is convex, solving the Rcone-programming problem arrives at a convergent solution. One design example is given to illustrate that the Rcone-programming-based formulation is simple, but it can get better design results than other conventional design approaches.