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

$$\Delta\in\left(\frac{N}{2}-\frac{1}{2},\frac{N}{2}+\frac{1}{2}\right),$$

where $N$ is the order of the interpolator.