# Digital Signal Processing/Hilbert Transform

## Definition

editThe Hilbert transform is used to generate a complex signal from a real signal. The Hilbert transform is characterized by the impulse response:

The Hilbert Transform of a function x(t) is the convolution of x(t) with the function h(t), above. The Hilbert Transform is defined as such:

[Hilbert Transform]

We use the notation to denote the Hilbert transformation of x(t).