Minimax Design of Low-Complexity Even-Order Variable Fractional-Delay Filters Using Second-Order Cone Programming

This brief proposes an optimal minimax method for designing even-order finite-impulse-response variable fractional-delay (VFD) digital filters by using the second-order cone programming (SOCP), which minimizes the peak error of the variable-frequency response and yields a true minimax design. To minimize the VFD filter complexity, we also present an algorithm for jointly optimizing all the subfilter orders in the Farrow structure such that all the subfilter orders can be simultaneously optimized for exactly meeting a given upper error bound. A design example is given to demonstrate the high performance and low complexity of the SOCP-based VFD filter.