We propose in this paper a new point of view which unifies two well known filter families for approximating ideal fractional delay filters: Lagrange Interpolator Filters (LIF) and Thiran Allpass Filters. We achieve this unification by approximating the ideal Fourier transform of the fractional delay according to two different Padé approximations: series expansions and continued fraction expansions, and by proving that both approximations correspond exactly either to the LIF family or to the allpass delay filters family. This leads to an efficient modular implementation of LIFs.