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:

:

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° ( 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