Complex Envelope [hlp]

You can read about it in any digital communication book. It is a representation of a compolex signal without carrier since carrier did not convay any information. In EDA tools, the circuit can be analyzed using this method to reduce simulation time.

equivalent lowpass signal of a bandpass signal is the complex envelope of that signal:
s(t)=a(t)*cos(wt+p(t))
complex envelope of s(t)= a(t)*exp(j*p(t))