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