Trigonometric interpolation

In mathematics, trigonometric interpolation is interpolation with trigonometric polynomials. Interpolation is the process of finding a function which goes through some given data points. For trigonometric interpolation, this function has to be a trigonometric polynomial, that is, a sum of sines and cosines of given periods. This form is especially suited for interpolation of periodic functions.

An important special case is when the given data points are equally spaced, in which case the solution is given by the discrete Fourier transform.

A trigonometric polynomial of degree K has the form

${\displaystyle p(x)=a_{0}+\sum _{k=1}^{K}a_{k}\cos(kx)+\sum _{k=1}^{K}b_{k}\sin(kx).\,}$

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