Generalized digital Butterworth filter design
Selesnick, I.W.; Burrus, C.S.
Signal Processing, IEEE Transactions on
Volume 46, Issue 6, Jun 1998 Page(s):1688 - 1694
Digital Object Identifier   10.1109/78.678493
Summary: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 closed-form 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 (monotonic) square magnitude frequency responses are maximally flat at ω=0 and at ω=π. Another result of the correspondence is that for a specified cutoff 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

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