Trigonometric interpolation

Summary

Trigonometric interpolation fits a trigonometric polynomial through prescribed values at given points of a period. With $2n + 1$ distinct nodes in one period there is exactly one interpolating trigonometric polynomial of degree at most $n$. It is the periodic counterpart of Lagrange interpolation by ordinary polynomials. For equally spaced nodes its coefficients are given by the discrete Fourier transform. This makes it fast to compute and central in numerical analysis and signal processing.