Folding band sharpening of the cascaded-integrator-comb filter results in a high passband droop. In applications requiring low passband deviation, the droop is reduced by connecting a low-order FIR compensator in cascade with the filter. In this Letter, the authors present a method for optimum design of compensators whose coefficients are expressed as sums of signed-power-of-two terms. The method is based on the minimisation of passband deviation, with specified total number of terms.

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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.

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