Phase (waves) - Formula

Formula

The phase of an oscillation or wave refers to a sinusoidal function such as the following:

\begin{align} x(t) &= A \cos( 2 \pi f t + \phi ) \\ y(t) &= A \sin( 2 \pi f t + \phi ) = A\cdot \cos\left( 2 \pi f t + \phi - \frac{\pi}{2}\right) \end{align}

where, and are constant parameters called the amplitude, frequency, and phase of the sinusoid. These functions are periodic with period, and they are identical except for a displacement of along the axis. The term phase can refer to several different things:

  • It can refer to a specified reference, such as, in which case we would say the phase of is, and the phase of is .
  • It can refer to, in which case we would say and have the same phase but are relative to their own specific references.
  • In the context of communication waveforms, the time-variant angle, or its modulo value, is referred to as instantaneous phase, often just phase.

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