Design and properties of polynomial-based fractional delay filters

Design and properties of polynomial-based FIR filters with adjustable fractional delay are studied. 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 one-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. The main benefit of the proposed synthesis scheme lies in the fact that it results in the structure where the linear-phase branch filters of the modified Farrow structure are fixed and only one parameter controls the fractional delay.