Constrained min-max optimization of multi-rate digital filters with simultaneous magnitude and group-delay specifications

This paper is concerned with the development of a new constrained min-max optimization technique for multi-rate digital filter transfer functions. The salient feature of this technique is that it can handle the simultaneous optimization of the magnitude/frequency and group-delay/frequency response characteristics for both finite and infinite precision transfer function coefficients. Moreover, it can handle not only inequality constraints (as in the case of existing approaches) but also equality constraints both on the magnitude/frequency and group-delay/frequency response characteristics. In addition, it is guaranteed to converge to a solution, of course, if a solution exists. The proposed optimization technique has been incorporated in a software package called Papillon I. The effectiveness and practical application of Papillon I is demonstrated by applying it to the optimization of a digital CODEC filter transfer function.