Quadrature phase

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Communication signals often have the form:

$A(t)\cdot \cos[\omega t + \phi(t)] \equiv I(t)\cdot \cos(\omega t) - Q(t)\cdot \sin(\omega t)\,$

where $\omega\,$ represents a carrier frequency, and:

$I(t) = A(t)\cdot \cos[\phi(t)]$

$Q(t) = A(t)\cdot \sin[\phi(t)]$

$A(t)\,$ and $\phi (t)\,$ represent possible modulation of a pure carrier wave: $\cos(\omega t)\,$ . The modulation alters the original $\cos\,$ component of the carrier, and creates a [new] $\sin\,$ 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° ( $\begin{matrix} \frac{\pi}{2} \end{matrix}$ radians) out of phase, is referred to as the quadrature component.