On frequency-domain and time-domain phase unwrapping

Time-domain phase unwrapping of analytic or complex functions of time is an unavoidable operation when processing such signals within an FM-modeling framework or when attempting to establish the instantaneous frequency of such signals. With the help of an alternate derivation of his equations, Tribolet's frequency-domain phase unwrapping algorithm is easily rewritten for time-domain application. The time derivative of the argument of the signal, a quantity needed in these modified equations, is developed and furthermore recognized to be proportional to the instantaneous frequency of the signal.