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Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase of a complex-valued function s, is the real-valued function:
where arg is the complex argument function.The instantaneous frequency is the temporal rate of change of the instantaneous phase.
And for a real-valued function s, it is determined from the function's analytic representation, sa:
where s ^ {\displaystyle {\hat {s}}} represents the Hilbert transform of s.
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