Maximally Flat Lowpass Filters from Allpass Sums

This paper describes a new class of maximally at lowpass recursive digital lters. These lters are realizable as a parallel sum of two allpass lters, a structure that has attracted much attention recently due to their applications in multirate ltering and the existence of low-complexity low-noise implementations of allpass lters. This class of lters can be made to have approximately linear phase in the passband, but it is not required. In addition, the continuous variation of the cut-oo frequency is described, and the classical Butterworth lter is retrieved as a special case. The construction of these lowpass lters depends upon a 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 specializes to a previously known result.