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Lagrange Interpolation Coefficient Symmetry

As shown in [504, §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:

$\displaystyle h_\Delta(n) \eqsp h_{N-\Delta}(N-n), \quad n =0,1,\ldots,N, \protect$ (5.8)

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


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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