On minimum/maximum/all-pass decompositions in time and frequency domains

We model a signal over T seconds by a pole-zero model by considering its periodic extensions. Using this model, we decompose the signal into its minimum-phase (MinP)/maximum-phase (MaxP) and all-phase (AllP) components. A simple algorithm for this decomposition that does not seem to have a counterpart in the cepstral literature is presented, This decomposition leads to representing signals by their envelope and instantaneous frequency that takes on positive values only. Nonperiodic signals can be processed by appropriately windowing the signals