A complex-error and phase-error constrained least-squares design of FIR filters with reduced group delay error

The group delay of a linear-phase FIR filter is about half of its length. Existing methods for low group-delay FIR filter design usually result in large group delay error, noticeably towards the band edges. Recently, Lai [2] presented a constrained least-squares design method that can specify both magnitude-error and phase-error upper bounds. Reduced group-delay error can be obtained by using a sigmoid phase-error upper-bound function in the method. In this paper, we improve the method by using a modified complex approximation error, such that we can more flexibly specify the magnitude and phase errors, and smaller magnitude error can be obtained under the same phase-error constraint. A multiple-exchange algorithm is used to solve the complex-error and phase-error constrained least-squares design problem. Through design examples, the proposed design method is compared with several existing method. Design examples demonstrate the effectiveness the proposed method.