Optimal design of minimum-phase FIR filters

The paper presents a new method for the optimal design of minimum phase FIR filters. First, a constrained approximation procedure is used to obtain the magnitude function and the transmission zeros in the stopband(s). Next, the zeros of the transfer function inside the unit circle are calculated via a low-degree polynomial factorization. For low-pass filters, a straightforward exchange algorithm is presented which achieves the constrained approximation step; a convergence proof is given and it is shown that the algorithm can be implemented via a simple modification of the Parks-McClellan program. The efficacy of the method is illustrated by a numerical example. Attention is drawn to the fact that bandpass filters may in principle require more sophisticated means.