### Explicit Lagrange Coefficient Formulas

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

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

*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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