傅里叶变换（法语：Transformation de Fourier、英语：Fourier transform）是一种线性的积分变换，常在将信号在时域（或空域）和频域之间变换时使用，在物理学和工程学中有许多应用。因其基本思想首先由法国学者约瑟夫·傅里叶系统地提出，所以以其名字来命名以示纪念。

经过傅里叶变换而生成的函数 称作原函数 的傅里叶变换、亦或其频谱。在许多情况下，傅里叶变换是可逆的，即可通过 得到其原函数 。通常情况下， 是实数函数，而 则是复数函数，用一个复数来表示振幅和相位。

“傅里叶变换”一词既可以指变换操作本身（将函数 进行傅里叶变换），又可以指该操作所生成的复数函数（ 是 的傅里叶变换）。

The Fourier transform decomposes a function of time (a signal) into the frequencies that make it up, similarly to how a musical chord can be expressed as the amplitude (or loudness) of its constituent notes. The Fourier transform of a function of time itself is a complex-valued function of frequency, whose absolute value represents the amount of that frequency present in the original function, and whose complex argument is the phase offset of the basic sinusoid in that frequency. The Fourier transform is called the frequency domain representation of the original signal. The term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of time. The Fourier transform is not limited to functions of time, but in order to have a unified language, the domain of the original function is commonly referred to as the time domain. For many functions of practical interest one can define an operation that reverses this: the inverse Fourier transformation, also called Fourier synthesis, of a frequency domain representation combines the contributions of all the different frequencies to recover the original function of time.