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

Famous quotes containing the word phase:

    “I had let preadolescence creep up on me without paying much attention—and I seriously underestimated this insidious phase of child development. You hear about it, but you’re not a true believer until it jumps out at you in the shape of your own, until recently quite companionable child.”
    —Susan Ferraro (20th century)