A class of comprehensive constraints for design of PCWLSE Laguerre and FIR filters: A boost in performance

The complex Chebyshev error criterion is usually used as a general constraint in design of peak constraint weighted least square error (PCWLSE) filters. It simply applies an upper bound on the maximum magnitude of error between the desired and designed transfer functions of the filter. It inherently confines the corresponding maximum phase error as well. However, it imposes an over restricted constraint on the problem which reduces the feasibility region of the filter design. Here a new and comprehensive class of constraints is proposed for the problem which provides a feasible region larger than that of the complex Chebyshev error constraint. Hence, the filter weights acquire larger space to search for better optimal values and consequently boost up the performance of the designed filter by achieving less weighted least square error (WLSE). Furthermore, the proposed constraints make no overlap or conflict between the desired magnitude, phase, and group delay bounds in design process. To achieve less computational complexity, the nonlinear constraints of the proposed approach have also been replaced with their equivalent linear approximations. Simulation results on the Laguerre and FIR filter structures show superiority of the proposed constraints over that of the complex Chebyshev error in achieving less WLSE.