Even-Order Lagrange Interpolation Summary

We may summarize some characteristics of even-order Lagrange fractional delay filtering as follows:

• Two-sample bounded-by-1 delay-range instead of only one-sample
• No gain zero at half the sampling rate for the middle delay
• No phase-delay discontinuity when crossing the middle delay
• Optimal (central) delay range is centered about an integer

To stay within the central, one-sample delay range for even-order Lagrange interpolators, the delay range should be

where is the order of the interpolator.

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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.