Digital Signal Processing/Hilbert Transform

DefinitionEdit

The 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).