Odd-order variable fractional-delay filters with generalized polygonal constraints

This paper presents a generalized minimax approach for designing odd-order finite-impulse-response (FIR) variable fractional-delay (VFD) digital filters using a regular polygon and analyzes the trade-off between the design time and design accuracy. The complex-valued frequency response errors are constrained inside a regular polygon, and the constrains are linear functions of the VFD filter coefficients. Hence, the minimax design can be solved by using the simple linear programming (LP) technique. For a given deviation from the true minimax design, we provide an analytical formula for determining the shape of the regular polygon such that the resulting minimax design is close to the true minimax design as specified. An example is given to show the effectiveness of the generalized polygonal approach.