Phase (waves)

Phase is the position of a point in time (an instant) on a waveform cycle. A complete cycle is defined as the interval required for the waveform to return to its arbitrary initial value. The graphic to the right shows how one cycle constitutes 360° of phase. The graphic also shows how phase is sometimes expressed in radians, where one radian of phase equals approximately 57.3°.

Phase can also be an expression of relative displacement between two corresponding features (for example, peaks or zero crossings) of two waveforms having the same frequency.

In sinusoidal functions or in waves "phase" has two different, but closely related, meanings. One is the initial angle of a sinusoidal function at its origin and is sometimes called phase offset or phase difference. Another usage is the fraction of the wave cycle that has elapsed relative to the origin.

Phase shift is any change that occurs in the phase of one quantity, or in the phase difference between two or more quantities.

This symbol: ${\displaystyle \varphi \,}$ is sometimes referred to as a phase shift or phase offset because it represents a "shift" from zero phase.

For infinitely long sinusoids, a change in ${\displaystyle \varphi \,}$ is the same as a shift in time, such as a time delay. If ${\displaystyle \scriptstyle x(t)\,}$ is delayed (time-shifted) by ${\displaystyle \scriptstyle {\frac {1}{4}}\,}$ of its cycle, it becomes:

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