Howtosignalprocessing
How do you find the complex envelope of a signal?
All the information carried in a real-valued signal s ( t ) can be represented by a corresponding lowpass complex envelope: s ( t ) = Re g ( t ) e j 2 π f c t = i ( t ) cos2 π f c t - q ( t ) sin2 π f c t . In this equation: f c is the carrier frequency.
Why do we need complex envelope?
The complex envelope is useful primarily for passband signals. In a lowpass signal the complex envelope of the signal is the signal itself. But in passband signal, the complex envelope representation allows us to easily separate out the carrier. We see the advantage of this form right away.
