The so-called
**analytic signal**
can be constructed from a real-valued time series *u*_{t} and
itself phase shifted, i.e., *v*_{t}
can be found using equation (5).
The analytic signal is *g*_{t},
where

(11) |

We can guess where the name ``**analytic signal**'' came from
if we think back to *Z*-transforms and causal functions.
Causal functions are free of **pole**s inside the unit circle,
so they are ``analytic'' there.
Their causality is the Fourier dual to the one-sidedness
we see here in the frequency domain.

A function is ``analytic'' if it is one-sided in the dual (Fourier) domain. |

10/21/1998