On the design of adjustable fractional delay FIR filters using digital differentiators

This paper proposes a systematic method to design adjustable fractional delay (FD) filters using the Farrow structure. The Farrow structure has even-order subfilters and the maximum magnitude approximation error determines the number of these subfilters. In the Farrow structure, different powers of the FD value are multiplied by the subfilters. As both the FD value and its powers are smaller than unity, they are considered as weighting functions. The approximation error for each subfilter can then increase in proportion to the power of the FD value. With the proposed design method, the first Farrow subfilter is a pure delay whereas the remaining subfilters are digital differentiators. Examples illustrate the proposed design method and comparison to some earlier designs shows an average reduction of 20% in arithmetic complexity.