# 18.10 Hilbert Transform (Pro Only)

This function calculates the Hilbert transform and/or the analytic signal which corresponds to the input.

Let f(ix) be the input signal, and let H() denote the Hilbert transform operator. The Hilbert transform of f(x) (denoted by g(y) below) can be defined as follows:

$g(y)=H(f(x))=\frac 1\pi \int_{-\infty }^\infty \frac{f(x)dx}{x-y} \,\!$

The result is actually a 90 degree phase shifted version of the input data, as shown in the graph below.

This function can also calculate the analytic signal corresponding to the input data. An analytic signal is a signal that has no negative frequency component. Let z(t) denote the analytical signal, then we have:

$z(t)=f(x)+jH(f(x)) \,\!$

##### To Use Hilbert Transform Tool
1. Make a workbook active.
2. Select Analysis: Signal Processing: Hilbert Transform from the Origin menu.
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