In the uniformly sampled case ( for some sampling interval ), a Lagrange interpolator can be viewed as a Finite Impulse Response (FIR) filter . Such filters are often called fractional delay filters , since they are filters providing a non-integer time delay, in general. Let denote the impulse response of such a fractional-delay filter. That is, assume the interpolation at point is given by
where we have set for simplicity, and used the fact that for in the case of ``true interpolators'' that pass through the given samples exactly. For best results, should be evaluated in a one-sample range centered about . For delays outside the central one-sample range, the coefficients can be shifted to translate the desired delay into that range.