Lagrange Interpolation Coefficient Symmetry

As shown in [502, §3.3.3], directly substituting into Eq.(4.7) derives the following coefficient symmetry property for the interpolation coefficients (impulse response) of a Lagrange fractional delay filter:

where is the order of the interpolator. Thus, the interpolation coefficients for delay are the ``flip'' (time reverse) of the coefficients for delay .

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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.