Phase (waves) - Phase Shift

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

is sometimes referred to as a phase shift or phase offset, because it represents a "shift" from zero phase. But a change in is also referred to as a phase shift.

For infinitely long sinusoids, a change in is the same as a shift in time, such as a time delay. If is delayed (time-shifted) by of its cycle, it becomes:

\begin{align} x\left(t - \frac{1}{4} T\right) &= A\cdot \cos\left(2 \pi f \left(t - \frac{1}{4}T \right) + \phi \right) \\ &= A\cdot \cos\left(2 \pi f t - \frac{\pi}{2} + \phi \right) \end{align}

whose "phase" is now . It has been shifted by radians.

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