Lowpass filters realizable as coupled allpasses: Design via a new flat delay filter

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