Bi-minimax design of odd-order variable fractional-delay digital filters

This paper presents a new minimax method called bi-minimax design for simultaneously suppressing the peak errors of variable frequency response (VFR) and peak errors of variable fractional-delay (VFD) of odd-order variable fractional-delay (VFD) filters. To achieve this goal, we minimize a compound error function that combines the two peak errors through a weighting factor. After linearizing the non-linear constraints on VFD errors, the minimax problem is solved by using the well-known software SeDuMi subject to both second-order cone (SOC) constraints and linear constraints. An odd-order example is given to illustrate the effectiveness of the odd-order bi-minimax design approach.