Generalized Digital Butterworth Filter Design
Selesnick, Ivan W.
Burrus, C. Sidney
This paper presents a formula-based method for the design of IIR filters having more zeros than (nontrivial) poles. The filters are designed so that their square magnitude frequency responses are maximally-flat at <i>m</i> = 0 and at <i>m</i> = <i>pi</i> and are thereby generalizations of classical digital Butterworth filters. A main result of the paper is that, for a specified half-magnitude frequency and a specified number of zeros, there is only one valid way in which to split the zeros between <i>z</i> = -1 and the passband. Moreover, for a specified number of zeros and a specified half-magnitude frequency, the method directly determines the appropriate way to split the zeros between <i>z</i> = -1 and the passband. IIR filters having more zeros than poles are of interest, because often, to obtain a good trade-off between performance and the expense of implementation, just a few poles are best.