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This paper introduces a novel solution to the problem of designing an economical adjustable wideband fractional delay (FD) filter. The innovation lies in an aggregation of two approaches aimed at obtaining a two-stage FD filter with reduced numerical complexity. The first approach is based on simultaneous optimization of sub-filters in one-stage arrangement. The second one makes use of two-rate technique to end up with an efficient single-rate structure. The novel design procedure entails joint minimax optimization of both stages and concurrently takes advantage of the benefits of the Farrow structure build up of fixed linear-phase sub-filters. Our filter requires a lower arithmetic complexity than the hitherto available ones, while meeting the same specification on the complex approximation error magnitude.