### Explicit Lagrange Coefficient Formulas

Given a desired fractional delay of samples, the Lagrange fraction-delay impulse response can be written in closed form as

 (5.7)

The following table gives specific examples for orders 1, 2, and 3:

Note that, for , Lagrange interpolation reduces to linear interpolation, i.e., the interpolator impulse response is . Also, remember that, for order , the desired delay should be in a one-sample range centered about .
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