Tricki
a repository of mathematical know-how

Use Fourier transforms to calculate derivatives

Stub iconThis article is a stub.This means that it cannot be considered to contain or lead to any mathematically interesting information.

Quick description

One can calculate the derivative of a function f(x) by calculating its Fourier transform \hat{f}(k), then calculating the inverse Fourier transform of ik\hat{f}(k) (where i is the square root of minus one). This method is tedious for analytic functions, but is very convenient if one needs to calculate the derivative of a function that is defined as a discrete data set.

Prerequisites

Fourier analysis

Example 1

General discussion