This paper has presented a new point of view for considering Lagrange Interpolator Filters applied to Fractional Delay Digital Filters approximations. This leads to a new closed form for the transfer function of LIFs, and to a new robust and efficient time-varying structure for the LIF implementation. Future works will compare the behavior of this structure to other classical structure such as the Farrow structure [7]. It will also involve a study for a fixed point implementation.