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Design and Multiplierless Implementation of Multirate Digital Filters Based on Sharpening Technique

The simplest multiplierless decimation filter is the cascaded-integrator-comb (CIC) filter proposed by Hogenauer in 1981. Since then, this filter remained dominant element in many applications containing multirate signal processing. However, the magnitude response of this filter has a high pass-band droop, which is often intolerable. The droop can be reduced by modifying the original CIC structure or by connecting an additional filter called CIC compensator in cascade with the CIC decimator. The CIC filter is a common part of digital-down converters. However, in processing of wideband signals, the CIC filter is often incapable of meeting the requirement for high folding-band attenuations. To improve the CIC-filter folding-band response, various structures have been developed. Efficient structures arise from the polynomial sharpening of CIC response. The most popular of them is proposed by Saramaki and Ritoniemi. This structure implements so called sharpened CIC (SCIC) filter. The design of sharpened CIC filters is based on searching the polynomial coefficients ensuring required magnitude response. Several design methods have been developed, resulting in real, integer, and sum-of-powers-of-two (SPT) coefficients. The latter is preferable since it results in multiplierless implementation. Two approaches to the design of sharpened CIC filters have been considered in literature. The first approach simultaneously sharpens the passband and the folding-band responses, whereas the second approach includes sharpening only within the folding bands. Well-established sharpening method was developed by Kaiser and Hamming. It results in maximally flat responses and it gives integer coefficients using analytic expression. Recently, Coleman proposed the application of the Chebyshev polynomials in the design of SCIC filters with very high folding- band attenuations. Furthermore, closed-form methods for the design of SCIC filters using the weighted least-squares and minimax error criterion in the passband and folding bands have been proposed. These methods provide SCIC filters ensuring small passband deviations and rather high folding-band attenuations. However, the coefficients obtained take real values, what results in the structure employing multipliers. Next, the particle swarm optimization has been used to calculate SPT polynomial coefficients in order to achieve a given passband deviation. Then, partially sharpened CIC filters have been developed, employing the polynomials in Bernstein's form. The proposed filters are multiplierless, but they only support power-of-two decimation factors. Later, the sharpening has been combined with passband compensation. Here, we present our work in design of multiplierless multirate digital filters based on sharpening technique. In particular, we describe an approach which employs a global optimization technique based on the interval analysis. We illustrate this approach by the design of multiplierless sharpened CIC filters with minimax error criterion in folding bands. The features of the presented approach are illustrated with the design of wideband SCIC filters.

multirate digital filters ; cascaded-integrator-comb filters ; sharpening ; sum-of-powers-of-two coefficients ; multiplierless ; minimax ; global optimization

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