A more sophisticated method of time alignment is the sinc convolution. The procedure as described above is an approximation for a system when it is in steady state. It does not consider the fact, that the system swings in and out.
Taking an ideal digital crossover and convolute the filters with a sinus chirp at the transition frequency produces an ideal waveform when added. Convoluting the same sinc with the measured response of the filters doesn’t. Optimization is done with modifying the signals rotation (e.g., time shift) and amplitude so that its swing-in and the periodic behaviour approximates the ideal one.
Let’s have a look at a practical example: The integration of a subwoofer. The transition frequency is 70Hz. The standard method shows quite some phase shift at the crossover frequency. When optimized with the sinc convolution, this improves dramatically.
The alternative procedure is a bit more time consuming, but worth the effort. The integration of the low frequency drivers into the sonic image is a great improvement.