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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:


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