Design of linear-phase partly digital anti-aliasing filters

A new approach is presented for the design of linear-phase anti-aliasing filters. These filters consist of an approximately linear phase analog filter cascaded with a linear phase nonrecursive digital decimator. The use of the decimation part enables us to use a higher sampling rate after the analog part. This increases the required transition bandwidth of the analog filter and, consequently, decreases the required filter order. The passband variation of the group delay response of the analog part is minimized subject to the given amplitude requirements. The optimization is done by an efficient iterative algorithm constructed using recent advances in constrained minimax optimization. As a decimator, we use a filter consisting of two parts, one working at the higher sampling rate and the other one at the final sampling rate. This filter requires significantly fewer multiplications per output sample than a conventional FIR decimator. Examples demonstrate that by oversampling by a factor of 3, a third order analog filter is sufficient to construct an extremely linear phase highly selective anti-aliasing filter meeting the same amplitude specifications as a seventh order purely analog elliptic filter.