Optimization and efficient implementation of FIR filters with adjustable fractional delay

An efficient design method is introduced for optimizing polynomial-based FIR filters with adjustable fractional delay. Given the passband region, the filter parameters are optimized to minimize in the passband the worst-case phase delay deviation from the desired value (the maximum deviation for fractional delays between zero and unity) subject to a given worst-case amplitude deviation from unity in the passband. It is shown that the filter with fractional delay equal to half determines the lower limit for the achievable amplitude distortion. Because the filters under consideration are polynomial-based, they can be efficiently implemented using the modified Farrow structure introduced by the authors.