Our paper has presented two new ways for deriving analytically Lagrange Interpolator Filters (LIF) and Thiran Allpass Filters from the ideal fractional delay filter. Both expressions logically lead to two fairly similar modular structures. As we have already shown in [7] it results for the LIF structure in a new robust efficient time-varying implementation. We get a new elegant theoretical closed form in the case of the allpass fractional delays.