Instantaneous Phase - Examples

Examples

Example 1: where and are positive values.
s_\mathrm{a}(t) = A\cdot e^{i (\omega t +\theta)} \,
In this simple sinusoidal, mono-frequency example, the constant is also commonly referred to as phase or phase offset. is a function of time. is not.
In the next example, we also see that the phase offset of a real-valued sinusoid is ambiguous unless a reference (sin or cos) is specified. is unambiguously defined.
Example 2:
s_\mathrm{a}(t) = A\cdot e^{i \left(\omega t -\begin{matrix} \frac{\pi}{2}\end{matrix}\right)} \,

In both examples the local maxima of correspond to for integer values of N. This has applications in the field of computer vision.

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