Design and Multiplierless Realization of Maximally Flat Sharpened-CIC Compensators

Polynomial sharpening is an efficient technique for improving folding band response of cascaded-integrator-comb (CIC) decimation filters. However, the sharpening of folding bands results in a high passband droop, which is intolerable in many applications. The droop can be reduced by connecting a symmetric finite-impulse-response filter called compensator in the cascade with the sharpened CIC (SCIC) filter. This brief presents a method for the design of such compensators, which is based on maximally flat error criterion. The compensator's coefficients are obtained by solving a linear system of equations which is formed using a straightforward procedure. The coefficients obtained generally take real values. However, we show that for the SCIC filters incorporating integer or sum of powers of two (SPT) polynomial coefficients, and whose decimation factors are expressed as powers of two, the coefficients of corresponding maximally flat compensators are integers or SPT representable. For these types of SCIC filters, the optimum multiplierless structures of the compensators with three and five coefficients are described.