A Matrix-based Algorithm for the LS Design of Variable Fractional Delay FIR Filters with Constraints

The design of variable fractional delay (VFD) finite-impulse response (FIR) filters with group delay error constraints in the least squares (LS) sense is investigated in this paper. Most of methods in the literature for designing VFD filters with constraints are based on vector variables, leading to a heavy computational load. To solve this problem more efficiently, we propose a matrix-based iterative constrained least squares (CLS) algorithm. By linearizing the highly nonlinear constraints as linear ones, the proposed algorithm transforms the original nonconvex design problem into a series of CLS subproblems. Each CLS subproblem is solved by using an efficient matrix-based active-set method. As a result, the proposed algorithm can fast converge to the LS solution with described group delay errors. Finally, design examples are provided to show the good performance of the proposed algorithm.