# Fourier Transform

A Fourier transform is a generalization of complex Fourier series that expresses a function in terms of frequency components. Fourier transforms arise quite commonly not only in mathematics, but also in optics, signal processing, and many other areas of science and engineering.

Fourier transform is a college-level concept that would be first encountered in a differential equations course.

### Prerequisites

Convolution: | Convolution is the integral transform that expresses the amount of overlap of one function g as it is shifted over another function f. |

Fourier Series: | A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines. |

Integral: | An integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals and derivatives are the fundamental objects of calculus. |