Variable Digital Filter With Group Delay Flatness Specification or Phase Constraints

In this paper, we consider the design of finite-impulseresponse variable digital filters (VDFs) with variable cutofffrequency or variable fractional delay. We propose the design ofVDFs with minimum integral squared error and constraints onthe maximum error deviation in conjunction with flatness groupdelay specification or phase constraints. These specifications allowthe VDFs to have approximately linear phase, especially in thepassband. As these specifications are required to be satisfied forall the filters generated by the VDF with controllable spectralcharacteristics, the linear constraints resulting from the flatnessspecification are relaxed to inequality constraints. To makethe optimization problem tractable for the phase constrainedproblem, suitable approximations are employed in the paper. Thedesign problem is formulated as an optimization problem witha quadratic cost function and infinite number of constraints. Anumerical scheme with adaptive grid step size is proposed forsolving the optimization problem.