If you're "measuring" a system and using SMAART etc... How does the software determine the phase of an individual box or driver?
When a dual channel Transfer Function measurement is generated, the reference signal is delayed to match with the measurement signal so that they can be compared. Because the measurement signal has a reference, we can tell timing information. When polarity is concerned, we match a systems polarity at a certain frequency, so two systems are in phase at that frequency but vary at others. This is why when you are matching the polarity of a subwoofer system to a main system you don't change the delay value in the analyzer - as the goal is to align the relative phase of the two systems, and match the polarity at your chosen frequency. Another example, if you are measuring two matched speakers, both of them will (ideally) be matched polarity at the frequency the 'delay tracker' has aligned to (we generally look to the 2-4khz range for emphasis on vocal intelligibility). The frequencies above the direct impulse will arrive sooner, and the frequencies below will arrive later - because the speaker elements are the same and have the same processing applied, also the phase traces will track each other well. That being said, if you have two speakers of different type, although they may be matched polarity at 2-4khz, the phase will not be matched at the adjacent frequencies, especially as frequencies get lower. An extreme example of this would be matching the polarity of a speaker which utilizes advanced processing to achieve a flat phase response, and one that doesn't. What I mean is a speaker whose frequencies from as low as 200Hz (or so) arrive at basically the same time as frequencies at 4000Hz and up, with a speaker which does not. Matching these two systems polarity at 2-4K is easy, but once you reach the next pass band, the phase response of the two systems will not even be close.
Basically, Polarity reversals can be spotted in both the phase trace (via a 180 degree offset) or in the Live Impulse Response (via a negative impulse in Lin view when Live IR is on - as frequencies get lower and lower they get harder and harder to view this way). However unlike the phase trace, Live IR can only show you time arrival information; ie direct arrival, and reflections thereafter - especially at high frequencies. The thing to take away is - when measuring the polarity of systems, you must choose a frequency at which point the systems are to be in phase and match the polarity at that frequency.
If you have downloaded the demo version of v7, or v7Di - perform some Transfer Function Measurements - turn Live IR on and zoom into the impulse of your measurement (right click and highlight the area of interest). Flip the polarity on the the system and observe the change in the Phase trace and Live IR. Be sure to take a look at the Getting Started documents to save yourself from getting bogged down from not being familiar with the interface. Most answers to any questions you will have starting out will be found within the documentation.
***shameless plug*** If you haven't already - look into taking a Smaart Training Seminar.
-edited to attempt to make the first paragraph a bit less confusing, probably in vain.