Group Delay

A relay race: treble crosses on time, bass lags by tau_g milliseconds, smearing the punch.

What it is

Group delay is how much later some frequencies leave a speaker than others, smearing timing and softening transients.

Key facts

• Definition: group delay = how long a band of frequencies is delayed; the negative slope of the phase-vs-frequency curve.
• Formula: tau_g(f) = -(1 / 360) x (d phi / d f), where tau_g = group delay in seconds, phi = phase in degrees, f = frequency in Hz.
• Units: seconds, but in pro audio always milliseconds (ms). 1 ms = 1/1000 s.
• Speed of sound in air = 343 m/s at 20 C; 1 ms of delay = 0.343 m = 34.3 cm of path difference.
• Audibility (Blauert and Laws): the ear is most sensitive around 2 kHz (~1 ms threshold), with ~1.5 ms at 4 kHz, ~2 ms at both 1 kHz and 8 kHz, and ~3.2 ms at 500 Hz, rising further in deep bass; sensitivity is a U-shaped curve, so bass smear is forgiven far more than midrange smear.
• Steeper filter = more group delay: a 24 dB/oct (4th-order Linkwitz-Riley) crossover smears more than 12 dB/oct (2nd-order); a 30-40 Hz sub high-pass can add 10-20 ms at the bottom octave.
• FIR (linear-phase) filters give FLAT group delay = zero smear but cost fixed latency (often 5-20 ms); IIR (analog-style) filters are cheaper, lower latency, but always add some group delay.
• Doubling power or sources = +3 dB; doubling SPL pressure = +6 dB; -3 dB = the half-power point used to spec crossover/bandwidth; +10 dB needed to sound twice as loud.
• Excess group delay = smear left AFTER subtracting pure propagation time; that is the part you hear as 'loose' or 'woolly'.
• Ported (bass-reflex) subs ring at their tuning frequency and have MORE group delay near tuning than sealed subs.

How it works

1. A speaker's phase shifts with frequency, not by the same amount everywhere.
2. Where phase changes fast with frequency, those bands arrive late = high group delay.
3. Crossovers and high-pass filters bend the phase curve hardest near their corner frequency.
4. Low frequencies physically take longer to develop, so subs sit a few ms behind the tops.
5. Stack enough delay and a kick's attack arrives smeared across several ms instead of one sharp hit.
6. Fix it with sub alignment delay, gentler filter slopes, or a linear-phase (FIR) processor.

Real examples

• Kick drum through a 4th-order 80 Hz crossover sounds 'woolly' because the sub band lags the punch by several ms.
• Ported sub ringing at its 35 Hz tuning leaves bass notes hanging instead of stopping clean.
• Tops time-aligned but subs not delayed: the slap of a snare arrives before its body = smeared transient.
• Switching a system processor from IIR to FIR linear-phase tightens the low end with no EQ change.
• A steep 30 Hz infrasonic high-pass adds 15 ms group delay and makes deep bass feel sluggish.

How it helps in live sound

• Measure it: use Smaart or REW, view the group-delay (or phase) trace, watch the crossover region.
• Add sub-to-top alignment delay (typically 2-15 ms) so the sub arrives WITH the tops, not before.
• Confirm alignment with a phase trace overlay: the two boxes should sit on top of each other through crossover.
• Prefer 24 dB/oct LR crossovers but know they cost group delay; drop to 12-18 dB/oct if the low end feels loose.
• Use FIR/linear-phase presets on DSP (Lake, Galileo, d&b ArrayProcessing) for tight kick at the cost of a few ms latency.
• Sealed subs over ported when transient tightness matters more than maximum low-end extension.