A Simplified Structure for FIR Filters with an Adjustable Fractional Delay

This paper introduces an efficient filter structure for implementing finite-impulse response (FIR) filters with an adjustable fractional delay. In this structure the first two subfilters are the same as in the modified Farrow structure, whereas the remaining ones are generated by properly combining these two subfilters with some additional very short filters, pure delay terms, adders, and multipliers. For significantly reducing the number of multipliers, the three-step synthesis scheme proposed by Yli-Kaakinen and Saramaki in the case of the modified Farrow structure is followed. First, the number of subfilters and their orders are determined such that the given criteria are sufficiently exceeded. Second, an initial filter is determined using a simple design scheme. This filter serves as a start-up solution for further optimization being performed using a constrained nonlinear optimization algorithm. Third, those coefficient values of the subfilters having a negligible effect on the overall system performance are fixed to be zero-valued. Both the performance and complexity of the proposed adjustable digital filters are compared with those of some existing adjustable FIR filters proposed in the literature. This comparison shows that, in the case of stringent amplitude and phase delay specifications, the number of multipliers for the proposed filters is less than 80 percent when compared with the corresponding optimized modified Farrow structure.