See Lagrange interpolators for the general form of the interpolator used in this article. <a href="https://en.wikipedia.org/wiki/Lagrange_polynomial" rel="nofollow">https://en.wikipedia.org/wiki/Lagrange_polynomial</a><p>There's a neater general formula for generating Lagrange interpolator polynomials of any order that avoids having to perform matrix inversion.<p>Interpolated values can be calculated in O(N) time, so Lagrange interpolation is always faster than FFT interpolation. Calculate the left Product(0..i-1) of each term in left-to-right order. If you carry the value from term to term, you only need one multiplication per term. and the Product(i+1..N-1) of each term in right-to-left order.<p>Lagrange interpolators with degrees that are close to Pi<i>N tend to be smoother, with less aliasing, when processing audio signals. (N=3, 6, 9, 13, &c). Truncating the Langrange polynomial is akin to windowing in FFT. Having an order that's roughly Pi</i>N ensures that the analogous window of the Langrange polynomial has smaller tail values.