A design method of minimum phase FIR filters with complex coefficients

In this paper, we present a directly design method of minimum phase FIR filters with complex coefficients using successive projections (SP) method. In general, it is necessary to restrict the zeros of transfer function inside the unit circle or on the unit circle to directly obtain the transfer function of minimum phase FIR filters. We use Rouche´s theorem for coefficient update algorithm in SP method to restrict the zeros of the transfer function inside the unit circle and on the unit circle. Therefore, the transfer function of minimum phase FIR filter is obtained without factorization by using the proposed method. Moreover, the proposed method is also able to obtain the transfer function of real coefficients by considering the imaginary part of complex coefficients as the zero. The usefulness of the proposed method is verified through some examples.