### Odd-Order Lagrange Interpolation Summary

In contrast to even-order Lagrange interpolation, the odd-order case has the following properties (in fractional delay filtering applications):
• Improved phase-delay accuracy at the expense of decreased amplitude-response accuracy (low-order examples in Fig.)
• Optimal (centered) delay range lies between two integers
The usual centered delay range is

which is between integers, and in this range, the amplitude response is observed to be bounded by 1. To avoid a discontinuous phase-delay jump at high frequencies when crossing the middle delay, the delay range can be shifted to

but then the gain may exceed 1 at some frequencies.
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