In this video Production Expert team member Julian Rodgers uses the Universal Audio IBP to fine tune the phase relationship between mics on a bass guitar using phase rotation.
The polarity invert button and its effect on the phase of an audio signal is well understood. By inverting the electrical polarity of the signal it gets inverted - the positive peaks become negative valleys and vice-versa. This results in a 180 degree phase shift.
Nearly as well understood is the effect the relative timing of two signals has on their phase relationship - it's important to understand that unlike amplitude, phase describes the relationship between two signals compared to each other. By delaying a signal against itself, comb filtering effects caused by destructive interference between these signals can be improved (or made worse) because of the effect this has on the signals' phase relationship. This is a frequency dependent effect (i.e. some frequencies are affected more than others for any given delay time).
Phase rotation is less well understood. By rotating the phase of a signal the level of the harmonics in that sound remain the same but their timing is altered. This is achieved using an All Pass filter. While the idea of a filter which doesn't "change the sound" seems counter-intuitive, it is easier to understand if you first appreciate that all analogue filters affect phase. This is implied by the fact that Linear Phase EQs exist. One of the reasons why different EQs sound different is their phase response. All an All Pass Filter is is a filter which only does the "phase bit".
If you want to know more about All Pass filters and their uses have a look at this excellent blog post from Dave Berners on the Universal Audio blog.
Dynamic Phase Rotation
The IBP video addresses static phasing issues. To see how you can address the constantly changing phase relationships which happen between the unrelated audio found in a typical multitrack session look at this video I did for Sound Radix's amazing Pi plug-in.
Pi goes beyond the fixed phase rotation offered by IBP and offers dynamic phase rotation, allowing use on uncorrelated signals, meaning that rather than fixing the phase relationships between multiple mics on a guitar amp or drum kit, it can be used on unrelated elements of a mix.
Phase rotation and the effect all conventional filters have on phase isn't spoken about as much as the more obvious effects of processors but together with distortion and time domain effects like transient response, phase rotation is responsible for a lot of the desirable effects of hardware and well-modelled software emulations. Very worth appreciating.