The so-called analytic signal can be constructed from a real-valued time series ut and itself phase shifted, i.e., vt can be found using equation (5). The analytic signal is gt, where
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 poles 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.|