I saw a couple of definitions for minimum-phase in different textbooks and I'm trying to understand what the implication of each of them. The first definition I saw was: An invertible system which both it and it's inverse are causal and (BIBO) stable. The second definition is: An invertible system which both it and it's inverse are causal and have finite energy. It was written in one textbook that had the second definition as an alternative to the first one that these constraints allow the system to have zeros and poles on the unit circle and I don't understand why (as opposed to the first def). just to make sure, I'm not restricting myself to rational systems. Another thing I saw in some textbook and didn't understand is that the second definition implied that the transfer function of the system and it's inverse are analytic in the exterior of the unit circle. So, to conclude, my questions are:
- why we have both of the definitions of minimum-phase?
- why the 2nd def implies that the system can have zeros and poles on the unit circle as opposed to the first def?
- why the 2nd def implies that the system and it's inverse have analytic transfer functions in the exterior of the unit circle?
Sorry for any grammar mistakes and thanks for any clarifications.