Iterative Procedures for the Designs of Multi-band FIR Filters with Reduced Group Delay Error

The finite impulse response (FIR) filter with constant low group delay has been widely used in many application areas, especially in the systems which require the filtered signal to have no phase distortion and low group delay. The phase response of the filter with low group delay can only be approximately linear, and its group delay can only be approximately constant. A procedure was recently introduced to gradually reduce the error between the designed and the desired group delays by updating the phase-error upper-bound function iteratively. However, the procedure has only been used to design single-band minimax FIR filters. In this paper, the procedure is modified such that it can be applied in the minimax and constrained least squares designs of multi-band FIR filters. Firstly, each passband is dealt with separately to effectively reduce the group delay error in each passband. Then, a balance is introduced to tradeoff the group delay errors in different passbands, resulting in further reduction of the largest group delay error in the whole passband. To guarantee feasible solutions to the constrained least-squares design, an inner loop is also introduced to reduce the convergence parameter of the procedure. Design examples demonstrate the effectiveness of the modified procedure in reducing the maximum group delay error of the multi-band FIR filters.