Digital Allpass Filters for Crossover Phase Equalization

When two loudspeaker drivers are crossed over we typically want their on-axis acoustic outputs to sum in-phase.  For example the 4th-order Linkwitz-Riley (LR4) crossover is designed for this.  In practice, however, things rarely work out so well because there are potentially many sources of (often nonlinear) phase distortion, e.g. equalization filters, physical offset of the drivers, band-pass characteristic of the drivers, and acoustical interaction with the baffle.

Crossover phase alignment is often corrected by delaying the signal to one of the drivers. This typically aligns the drivers’ acoustic phases only up to zeroth-order, which is a bit rough.  It’s possible to do much better: one can design an allpass phase-equalization filter that gives accurate alignment throughout the crossover region.  My aim here is to briefly demonstrate the technique. Continue reading