I read that any system with a time delay cannot be minimum phase. As all real world systems have physical length over which a signal must propagate, does this mean that real world filters etc. Cannot be minimum phase?
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Yes and no.
That's a bit of a philosophical question: all mathematical models we make of the physical world are approximate in nature. You choose the model that's a good balance between complexity and the required accuracy for the problem at hand. There are no such things like "ideal resistors" or "ideal sine waves" but yet they are useful concepts and "good enough" approximation for stuff we see in the real world.
Many physical systems can be modelled as "minimum phase" with perfectly satisfactory results since the residual amount of "non-minimum-phasiness" can be neglected.
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$\begingroup$ Excellent point and I haven’t really thought about how a minimum phase system has all its poles and zeros in the left half plane (or inside unit circle) but that’s not the definition and you can have a system with all poles and zeros in left half plane but still not be minimum phase by simply delaying it! (Well I guess the case I am thinking of has a zero or zeros at infinity so I guess that is the out) $\endgroup$ Commented Jul 12 at 23:08
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1$\begingroup$ @DanBoschen actually the system has a $e^{-t_d s}$ term in the numerator, which means it has an infinite number of zeros on the imaginary axis -- which means it has zeros outside of the left-half plane. $\endgroup$ Commented Jul 13 at 2:12
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$\begingroup$ @TimWescott yes, good point! I was thinking of the cases where we delay by a unit sample or samples but even for those on the s-plane what you say would apply… and then for the z-plane there is also no confusion that the zero or zeros at infinity would clearly be outside the unit circle so seems like the pole zero test is still universally applicable- thanks! (You just need to be sure you are including all which means if you don’t see the same number of poles and zeros then there are roots at infinity) $\endgroup$ Commented Jul 13 at 13:05
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1$\begingroup$ @DanBoschen: I think the whole "philosophical" part doesn't apply to time discrete systems. Time discrete systems are already an abstraction of the physical world and all the relevant simplifications have been made at the conversion from continuous to discrete. Discrete systems can be perfectly minimum phase. They just don't represent a real physical system (without some amount of approximation). $\endgroup$– HilmarCommented Jul 14 at 12:34
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$\begingroup$ ....which brings in the philosophical part ;) but the OP's question (and the details of your response) is a good observation. $\endgroup$ Commented Jul 14 at 15:26