Instantaneous Phase

The notions of instantaneous phase and instantaneous frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions.

The instantaneous phase (or "local phase" or simply "phase") of a complex-valued function is the real-valued function

\phi(t) = \arg(x(t)).\, (See arg function.)

And for a real-valued function, it is determined from the function's analytic representation, :

\phi(t) = \mathrm{arg}( s_\mathrm{a}(t) ) .\,

When is constrained to an interval such as or it is called the wrapped phase. Otherwise it is called unwrapped, which is a continuous function of argument assuming is a continuous function of Unless otherwise indicated, the continuous form should be inferred.

Read more about Instantaneous Phase:  Examples, Instantaneous Frequency, Complex Representation

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