Design of Minimum-length, Minimum-phase, Low-Group-Delay FIR Filter Using Convex Optimization Method

This paper proposes a new method for optimal design of minimum-length, minimum-phase, low-group-delay FIR filter by employing convex optimization, discrete signal processing (DSP), and polynomial stabilization techniques. The design of a length-N FIR filter is formulated as a convex second-order cone programming (SOCP). In order to design a minimum-phase FIR filter as the necessary condition for having low group delay, the algorithm guarantees that all the filter’s zeros are inside the unit circle (minimum-phase). In addition, the quasiconvex optimization problem is developed to minimize the length of minimumphase, low-group-delay FIR filter. To this end, for a typical low-pass FIR filter, the length of the filter is minimized such that the optimum magnitude response is satisfied, the minimum-phase characteristic is maintained, and the low-group-delay is achieved. The proposed design algorithm only relies on one parameter (cut-off frequency) and the rest of filter parameters are automatically optimized as the trade-off between having minimum-length, minimum-phase, maximum stopband attenuation and low group delay. The effectiveness and performance of proposed approach is demonstrated and compared with other approaches over a set of examples. It is illustrated that this approach converges to the optimal solution in a few iterations.