It has been seen that the ideal FDDF can not be realized and it must be approximated in some way. Several solutions had been developped over more than fifty years (see [2]). Each implementation has its advantages and its drawbacks, and the best solution depends on the type of application. Until now Lagrange Interpolators Filters (LIFs) have been used because of their simplicity and their FIR structure. But their implementation relied heavily on the order of the filter, and the update parameter cost is prohibitive in delay-varying applications. The power series expansion of the ideal FDDF leads to a new kind of FIR approximation which reveals itself to be exactly LIFs. Moreover the modularity displayed in the new formulation results in a pretty implementation for LIFs.