Quadrature phase

Communication signals often have the form:

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

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

: $I(t)cdot sin(2pi ft) + Q(t)cdot underbrace{cos(2pi ft)}_{sinleft(2pi ft + egin{matrix} frac{pi}{2} end{matrix}
ight)},$

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

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

$A(t),$ and $phi (t),$ represent possible modulation of a pure carrier wave: $sin(2pi f t).,$ 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° ( $egin{matrix} frac{pi}{2} end{matrix}$ radians) out of phase, is referred to as the quadrature component.

Notes

See also

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

Quadrature phase

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