Linear-Phase Room Correction: The Trade-Offs

Every speaker delays its bass relative to its treble. The box rolls off below its tuning and the crossover splits the band, and both are filters that shift the phase of the frequencies around them. The result is excess group delay: about 5 ms for a sealed box rolling off at 50 Hz, 15 to 20 ms for a ported box at 35 Hz, and about 0.2 ms at a 2 kHz crossover.

A phase-inverse FIR filter applies the mirror image of that delay. It cannot make the bass arrive sooner, because no real-time filter can output a sound before it receives it. It holds back the treble and midrange instead, until they arrive as late as the bass. The filter's latency is therefore set by the frequency with the most group delay.

Linear phase

A response whose group delay is the same at every frequency. It is a pure delay plus whatever magnitude shaping the filter applies.

Linearising a speaker costs latency that grows as the corner falls. A phase-inverse FIR needs 0.8 ms for a 2 kHz crossover, 19 ms for an 80 Hz sub crossover, 31 ms for a sealed box rolling off at 50 Hz and 82 ms for a ported box at 35 Hz, measured as pre-response to -60 dB. Latency does not matter for playback, but it does when you hear yourself through the system, as in tracking.

A linear-phase filter's impulse response is symmetric in time, so any ringing it adds appears before the transient as well as after it. The plot at the top of this page shows it for a single 10 dB cut at 60 Hz: the linear-phase version starts moving about 50 ms before the hit. A minimum-phase filter with the same magnitude response rings only after the hit, where the room's own decay already sits.

Pre-ringing arrives before the transient that would otherwise mask it. None of the sources behind this series measures when it becomes audible, so judge a linear-phase correction on kicks and plucks at matched level.

A speaker's own excess phase, from its box and crossover, is much the same anywhere in front of it. A measurement at the listening position also captures the room, and above 1 to 2 kHz the measured phase includes the room's reflections, and a 5 cm head movement changes a path's phase by 105 degrees at 2 kHz. A correction that inverts the phase at the microphone leaves a phase error at every head position other than the microphone's.

The target that holds across the listening area is therefore the speaker's own excess phase, not the room's. A correction aimed at the speaker therefore covers the box roll-off and the crossovers.

Weigh each feature against what it buys. A 2 kHz crossover adds about 0.2 ms of group delay. Blauert and Laws (1978) found listeners needed about 1 ms of variation near 2 kHz before they could detect it, and the group delay study puts a modelled two-way, from 200 Hz up, at 0.10 times the threshold at its worst frequency, before any correction. Linearising it still costs 0.8 ms of latency, so the filter adds delay to remove a difference below what listeners detected. The bass cases are where the excess group delay is large, and they are also where the filter is longest, the pre-ringing reaches furthest and the audibility of the original problem is least certain.

Our recommendation: if your monitors are sealed, skip linear-phase correction. The study puts a modelled sealed two-way at 0.14 times the threshold if it scales with the period below 500 Hz and 1.29 times if it is held at 3.2 ms, and removing it costs 31 ms. If you mix on ported speakers, only play back through the system, and never track through it, a bass-only linear-phase correction is a reasonable experiment. Judge it on transients at matched level.

An IIR all-pass filter cannot flatten the bass group delay at low latency either. The reason is in Where the Latency in Linear-Phase Room Correction Comes From, and what NEXUS and Omnissiah do instead is in Phase in NEXUS and Omnissiah.