Digital Signal Processing/Hilbert Transform



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).