Phase (waves) - In-phase and Quadrature (I&Q) Components

In-phase and Quadrature (I&Q) Components

See also: Quadrature phase and Constellation diagram

The term in-phase is also found in the context of communication signals:

A(t)\cdot \sin = I(t)\cdot \sin(2\pi ft) + Q(t)\cdot \underbrace{\sin\left(2\pi ft + \begin{matrix} \frac{\pi}{2} \end{matrix} \right)}_{\cos(2\pi ft)}

and:

A(t)\cdot \cos = I(t)\cdot \cos(2\pi ft) + Q(t)\cdot \underbrace{\cos\left(2\pi ft + \begin{matrix} \frac{\pi}{2} \end{matrix}\right)}_{-\sin(2\pi ft)},

where represents a carrier frequency, and

\begin{align} I(t) &\equiv A(t)\cdot \cos\left(\phi(t)\right) \\ Q(t) &\equiv A(t)\cdot \sin\left(\phi(t)\right) \end{align}

and represent possible modulation of a pure carrier wave; e.g., (or ). The modulation alters the original (or ) component of the carrier, and creates a (new) (or ) 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.

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