Weighted least-squares design of sharpened CIC filters

Efficient multiplierless decimation filter is the cascaded-integrator-comb (CIC) filter. However, in many applications its magnitude response does not meet the requirement for selectivity. One technique for improving the response is sharpening. This technique results in filters having very low passband droop and high folding-band attenuations. The sharpening was first proposed by Kaiser and Hamming. They presented the polynomial amplitude-change function that is obtained by imposing flatness at the points (0,0) and (1,1). In this paper, we present a method for the design of sharpened CIC filters which is based on weighted least-squares error criterion. The method is given in a closed form which provides the optimum polynomial coefficients analytically. The filters presented are suitable for application in narrowband and wideband software radio receivers.