Multiplierless decimation filters based on amplitude sharpening and compensation
Aljoša Dudarin · 2019
The simplest multiplierless decimation filter is the cascaded-integrator-comb (CIC) filter. However, CIC filters introduce a passband droop, which is intolerable in many applications. The droop can be reduced by connecting a linear-phase finite-impulse-response filter called compensator in cascade with CIC filter. Since CIC filters are multiplierless, CIC compensators with multiplierless structures are preferable. In the thesis, two methods for the design of multiplierless CIC compensators have been proposed. Both methods are based on minimization of the maximum passband deviation. However, the first method provides an efficient compensation by using coefficients expressed as sums of powers of two (SPT), whereas the second method brings simple compensator's structures by representing each coefficient as signed power of two. In both approaches, the optimum coefficients are found by using global optimization. In processing of wideband signals, CIC filter is often incapable of meeting the requirement for high folding-band attenuations. To improve CIC filter folding-band response, various structures have been developed. An efficient structure arises from polynomial sharpening of the folding-band response. This structure implements a so-called sharpened CIC (SCIC) filter. To obtain very high folding-band attenuations of SCIC filters, the minimax sharpening of the folding bands is proposed. In addition, to obtain multiplierless SCIC structures, polynomials with SPT coefficients are used. However, the SCIC response also introduces a high passband droop. The droop can be reduced by connecting a compensator in cascade with the SCIC filter. For the multiplierless SCIC filters, multiplierless compensators are preferable. In the thesis, two approaches for design of multiplierless SCIC compensators are proposed. The first approach brings a closed-form method based on maximally flat approximation. Such an approximation is suitable for narrowband SCIC filters. The second approach results in a global method based on the minimization of the maximum passband deviation. This method is preferable for wideband SCIC filters.