14
Complex Baseband-equivalent Description of Bandlimited Signals
A bandlimited real-valued signal can be characterized by means of the following formula
where ω0 stands for the carrier frequency, a(t) represents the amplitude of the signal and ϕ(t) denotes the corresponding phase. All of these parameters are real-valued. v(t) can be split into two parts in the following way
where
are the so called in-phase and quadrature-phase components, respectively. The two components together are referred to as quadrature components.
Since vI (t) and vQ(t) are independent from the carrier frequency let us introduce the complex baseband equivalent of v(t)
which is the same as
This ‘virtual’ description can be used between the endpoints without including the carrier and since we are interested in the real signal in the receiver we can apply the following relations
or equivalently
The next problem ...
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