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 signals is the real-valued function:
-
(see arg function)
And for a real-valued signal 
it is determined from the signal's analytic representation, 
:
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.
from wiki