Lowpass Filters Realizable as Allpass Sums: Design via a New Flat Delay Filter

This paper describes a new class of maximally at lowpass recursive digital lters. The lters are realizable as a parallel sum of two allpass lters, a structure for which low-complexity low-noise implementations exist. Note that, with the classical Butterworth lter of degree N, which is retrieved as a special case, it is not possible to adjust the delay (or phase-linearity). However, with the more general class of lters described in this paper, the adjustment of the delay becomes possible, and the trade-oo between the delay and the phase-linearity can be chosen. The construction of these lowpass lters depends upon a new maximally at delay allpole lter, for which the degrees of atness at ! = 0 and ! = are not necessarily equal. For the coeecients of this at delay lter, an explicit solution is introduced, which also specializes to a previously known result.