Here are different phase operations for comparison. This digram shows the frequency domain as
phase is part of the frequency domain view of things.
green: The "
original", in this case a nearly ideal phase curve, very close to constant phase ≈ 0°
blue:
phase shift (180°), at each frequency the phase is changed a fixed amount (of angle)
pink: delay (7ms), the phase changed is frequency dependent, higher frequency -> greater phase change
red: this is how the phase looks most of the time. This is neither a constant phase change nor a constant delay.
A delay will create too much phase shift in higher frequency, a phase shift (i.e.180° =3,142 rad polarity switch) creates too much phase shift in other regions.
View attachment 450331
The point being of course that the phase curves for sub and main will be different.
It is necessary to bring the phase curves in the crossover regions on top of each other. Nice to have is a phase curve that is close to constant (≈0°).
For this alignment it is necessary to have
A. time alignment (impulses start at the same time)
and
B. phase alignment (sound from sub and main "work together" instead of canceling.
The problem is that
changing the phase will change the time alignment, because in the region of the phase change there will be
created a group delay.
And the "correction" with a
delay will create a
phase change in all frequencies and not a constant one.
And last there are phase deviations that cannot corrected with neither method and (inverted) all pass filters are necessary.
To reach alignment one probably needs some iteration with going back and forth between time domain (delay) and frequency domain (phase) until it fits convincingly.
For time alignment the use of wavelets with a tapered leading edge is not necessarily helpful as the start will be hard to gauge and the impulse peak (envelope) is corrupted by reflections (in "small" listening rooms) and will not give the correct delay.
For phase alignment a wavelet with narrow bandwidth (and tapered leading edge) IS helpful.