Generalized digital butterworth filter design

This correspondence introduces a new class of infinite impulse response (IIR) digital filters that unifies the classical digital Butterworth filter and the well-known maximally flat FIR filter. New closedform expressions are provided, and a straightforward design technique is described. The new IIR digital filters have more zeros than poles (away from the origin), and their (monotonie) square magnitude frequency responses are maximally flat at u = 0 and at u = TT. Another result of the correspondence is that for a specified cut-off frequency and a specified number of zeros, there is only one valid way in which to split the zeros between z = -1 and the passband. This technique also permits continuous variation of the cutoff frequency. IIR filters having more zeros than poles are of interest because often, to obtain a good tradeoff between performance and implementation complexity, just a few poles are best.