Phase difference

For shifted signals

The phase difference is especially important when comparing a periodic signal ${\displaystyle F}$ with a shifted and possibly scaled version ${\displaystyle G}$ of it. That is, suppose that ${\displaystyle G(t)=\alpha \,F(t+\tau )}$ for some constants ${\displaystyle \alpha ,\tau }$ and all ${\displaystyle t}$. Suppose also that the origin for computing the phase of ${\displaystyle G}$ has been shifted too. In that case, the phase difference ${\displaystyle \varphi }$ is a constant (independent of ${\displaystyle t}$), called the 'phase shift' or 'phase offset' of ${\displaystyle G}$ relative to ${\displaystyle F}$. In the clock analogy, this situation corresponds to the two hands turning at the same speed, so that the angle between them is constant.