Algorithm for decomposing an analytic signal into AM and positive FM components

An analytic signal permits unambiguous characterization of the phase and envelope of a real signal. But the analytic signal´s phase-derivative, i.e. the instantaneous frequency (IF) is typically a wild function and can take on values ranging from negative infinity to positive infinity. Fortunately, any analytic signal can be decomposed into a minimum phase (MinP) signal component and an all-phase (AllP) signal component. While the MinP signal´s log-envelope and its phase form a Hilbert transform pair, the AllP signal has a positive definite instantaneous frequency (PIF) unlike that of the original analytic signal. We propose an elegant computational algorithm that separates the MinP and AllP components of the analytic signal. The envelope of the MinP component corresponds to the AM and the PIF of the AllP component corresponds to the positive FM