Fourier analysis

Summary

Fourier analysis is the study of how functions are represented by sums or integrals of sines, cosines and complex exponentials. Its main tools are the Fourier series of periodic functions, the Fourier transform on $\R^n$ and the discrete Fourier transform on $\Z / N\Z$. It is the classical core of harmonic analysis. It turns differentiation into multiplication and convolution into pointwise product, which makes it central for differential equations and signal processing.