在数学与信号处理的领域中，一个实数值函数的希尔伯特转换(Hilbert transform)——在此标示为——是将信号与做卷积，以得到。因此，希尔伯特转换结果可以被解读为输入是的线性非时变系统(linear time invariant system)的输出，而此一系统的脉冲响应为。这是一项有用的数学，用在描述一个以实数值载波做调制的信号之复数包络(complex envelope)，出现在通信理论（应用方面的详述请见下文。）

希尔伯特转换是以著名数学家大卫·希尔伯特(David Hilbert)来命名。

In mathematics and in signal processing, the Hilbert transform is a linear operator that takes a function, u(t), and produces a function, H(u)(t), with the same domain.

The Hilbert transform is important in signal processing, where it derives the analytic representation of a signal u(t). This means that the real signal u(t) is extended into the complex plane such that it satisfies the Cauchy–Riemann equations. For example, the Hilbert transform leads to the harmonic conjugate of a given function in Fourier analysis, aka harmonic analysis. Equivalently, it is an example of a singular integral operator and of a Fourier multiplier.