Communication signals often have the form:

:$A\left(t\right)cdot sin \left[2pi ft + phi\left(t\right)\right] ,$ which is called "envelope-and-phase" form.

An equivalent representation, called "quadrature-carrier" form, is:

:

where $f,$ represents a carrier frequency, and:

:$I\left(t\right) stackrel\left\{mathrm\left\{def\left\{=\right\} A\left(t\right)cdot cos \left[phi\left(t\right)\right] ,$:$Q\left(t\right) stackrel\left\{mathrm\left\{def\left\{=\right\} A\left(t\right)cdot sin \left[phi\left(t\right)\right] .,$

$A\left(t\right),$ and $phi \left(t\right),$ represent possible modulation of a pure carrier wave: $sin\left(2pi f t\right).,$ The modulation alters the original $sin,$ component of the carrier, and creates a (new) $cos,$ component, as shown above. The component that is in phase with the original carrier is referred to as the "in-phase component". The other component, which is always 90° ( radians) out of phase, is referred to as the quadrature component.

Notes

Phase (waves)#In-phase and quadrature (I&Q) components

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