Trigonometric Interpolation Using the Discrete Fourier Transform

Abstract

The Fourier transform (and all its versions, discrete/continuous/finite/infinite), covers deep and abstract mathematical concepts, and can easily overwhelm with detail. In this paper I provide some intuitive ideas of how the discrete Fourier transform (and its version with low frequencies) works and how we can use it to approximate real periodic functions and parametric closed curves by means of trigonometric interpolation.