Design of Mth-band FIR Linear Phase Filters

This paper proposes an improved method for the Chebyshev approximation of Mth-band FIR linear phase filters using the Remez exchange algorithm. It is known from the time-domain condition that the magnitude responses of Mth-band FIR filters are dependent on each other in passband and stopband. In the conventional method, the Remez exchange algorithm was applied only in stopband to minimize the stopband error [8]. In this paper, the Remez exchange algorithm is applied in passband and a part of stopband to improve the magnitude response. In the proposed method, the filter coefficients are computed only by solving a set of linear equations, and the optimal coefficients can be easily obtained through a few iterations. The proposed method is more computationally efficient than the existing methods.