### Interpolation of Uniformly Spaced Samples

In the uniformly sampled case ( for some sampling interval
), a Lagrange interpolator can be viewed as a Finite Impulse
Response (FIR) filter [449]. Such filters are often called
*fractional delay filters*
[267], 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.

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Fractional Delay Filters

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Large Delay Changes