---
date: '2024-12-17'
description: the idea of any complex signals can be decomposed into simplifer sin waves.
id: Fourier transform
modified: 2026-06-05 15:08:04 GMT-04:00
tags:
  - math
title: Fourier transform
created: '2024-12-17'
published: '2024-12-17'
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---
_the idea of any signals in time domain can be decomposed into sinusoidal components_

> \[!definition\] Definition 1.
>
> The Fourier transform is given by the following:
>
> $$
> \displaystyle {\widehat {f}}(\xi )=\int _{-\infty }^{\infty }f(x)\ e^{-i2\pi \xi x}\,dx
> $$