### Even-Order Lagrange Interpolation Summary

We may summarize some characteristics of even-order Lagrange fractional delay filtering as follows:

• Two-sample bounded-by-1 delay-range instead of only one-sample
• No gain zero at half the sampling rate for the middle delay
• No phase-delay discontinuity when crossing the middle delay
• Optimal (central) delay range is centered about an integer
To stay within the central, one-sample delay range for even-order Lagrange interpolators, the delay range should be

where is the order of the interpolator.

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Lagrange Frequency Response Magnitude Bound