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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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.