Decimation filters with minimum number of additions per output sample

Abstract

In multistage decimation filters some stages operate at the low sampling rate, thus reducing the required number of additions per output sample (APOS). State-of-the-art methods for the design of these filters usually consider only two stages. In addition, these methods do not optimize the number of APOS explicitly. This Letter proposes a framework for the design of multistage decimation filters with minimum number of APOS. To accomplish this task, the structures which contain maximum number of stages allowed by specified decimation factor are optimized. As a case study, multistage filters whose stages are cascaded-integrator-comb filters are considered. It is illustrated by several examples that the proposed optimum filters ensure smaller number of APOS and higher folding-band attenuation than those obtained by recent methods for multistage filter design.