Linear Programming-Based Minimax Design of Odd-Order Variable Fractional-Delay Filters

This paper formulates an approximate linear programming (LP) approach to the minimax design of odd-order finite-impulse-response (FIR) variable fractional-delay (VFD) digital filters. The basic idea is to constrain the complex-valued frequency response errors of an odd-order VFD filter inside a hexadecagon. This converts non-linear constraints into linear ones and thus nearly-optimal minimax design can be achieved by using an LP technique. An odd-order design example is given to verify the effectiveness of the hexadecagonally constrained minimax design technique.