Allpass VFD Filter Design

This correspondence proposes a general design for allpass variable fractional delay (VFD) digital filters with minimum weighted integral squared error subject to constraints on maximum error deviation from the desired response. The resulting optimization problem is nonlinear and nonconvex with a nonlinear continuous inequality constraint. Stability of the designed filters are discussed. An effective procedure is proposed for solving the optimization problem. Firstly, a constraint transcription method and a smoothing technique are employed to transform the continuous inequality constraint into one equality constraint. Then, by using the concept of a penalty function, the transformed constraint is incorporated into the cost function to form a new cost function. The nonlinear optimization problem subject to continuous inequality constraints is then approximated by a sequence of unconstraint optimization problems. Finally, a global optimization method using a filled function is employed to solve the unconstraint optimization problem. Design example shows that a trade-off can be achieved between the integral squared error and the maximum error deviation for the design of allpass VFD filters.