What exactly is a complex envelope?

I have seen this be mentioned a couple of times in some books I read, so I want to make sure. Is the complex envelope simply the summation of the real and quadrature components of a signal, whereby the absolute value is the (real) envelope? I have read this wiki page but I am not sure I completely understand. Is the complex envelope simply the real and imaginary parts of a passband signal combined? Thank you.

Depends on context.

For strictly real-valued signals it sometimes refers to creating an analytic signal (see: http://en.m.wikipedia.org/wiki/Analytic_signal ) from a signal with no imaginary component, and taking the magnitude (or complex with both magnitude and phase) envelope of that hypothetical now complex creation.

• But if the envelope is real, then why do they call it a complex envelope? What is complex about it? – TheGrapeBeyond Jul 29 '13 at 20:52
• The signal is no longer real after adding the Hilbert transform imaginary component to make it complex and (pseudo) analytic. – hotpaw2 Jul 29 '13 at 20:55
• So the complex envelope is the analytical signal then? – TheGrapeBeyond Jul 30 '13 at 14:30
• Yes, complex envelope is an analytic signal. Your question had the answer partially in it. It is not just the summation of Real and Quadrature components, it's the summation of Real and j*Quadrature Component thereby creating an analytic signal. The envelope is just the magnitude of the analytic signal. When you talk in terms of communication systems, the Baseband signal is the Analytic function representing the signal at "Baseband" frequencies. – Sudarsan Aug 28 '13 at 22:55