Lagrange Interpolation Coefficient Symmetry

As shown in [506, §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:

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