Delay-error-constrained minimax design of all-pass variable-fractional-delay digital filters

This paper first derives a simplified variable-fractional-delay (VFD) expression for the all-pass (AP) VFD digital filter, and then uses the simplified VFD expression to formulate the minimax AP-VFD filter design as a two-step linear-programming (LP) problem. To suppress the maximum error of the VFD response (VFD-peak-error), this minimax design minimizes the maximum error of the variable-frequency-response (VFR) subject to the VFD-peak-error constraint. Thus, this two-step design can minimize the VFR-peak-error with the VFD-peak-error suppressed below a prescribed upper bound. With the aid of the simplified VFD expression, the VFD-peak-error constraint can be approximately linearized as a linear one, and thus the minimax design can be solved by using the LP method. We will use an illustrative example to verify that the simplified VFD expression is almost the same as the true one, and that the proposed LP-based two-step minimax design can significantly suppress the VFD-peak-error.