Linear phase vs minimum phase EQ

At a glance

What's the difference between linear phase and minimum phase EQ?

An EQ curve tells you how much each frequency gets turned up or down. It says nothing about when each frequency comes out, and the same curve can be built in more than one way that answers that question differently. Minimum phase and linear phase are the two common answers, and they're all that changes when you flip the phase mode on an EQ such as FabFilter Pro-Q.

A minimum phase EQ behaves like an analogue circuit. Its filters work on each sample as it arrives, feeding a little of their own output back into themselves, so there's no latency. The side effect is that the frequencies around each change fall slightly out of step with the rest, mostly later and sometimes a touch earlier. That timing change is called phase shift, and it's why the mode has the name it does: of all the filters that could draw a given curve, this kind has the least delay.

A linear phase EQ uses one long filter whose response to a click is the same forwards as backwards. Every frequency comes out late by exactly the same amount, so nothing in the sound moves against anything else, and your DAW lines the whole track back up with the others. Plot phase against frequency for such a filter and you get a straight line, hence linear.

The first two steps of the lab put a 24 dB per octave low cut at 100 Hz on the drums in each mode. In minimum phase the lane under the curve bends around the cutoff, with the drums near 87 Hz coming out 6.2 ms late. In linear phase the lane is flat and the whole sound is 92.9 ms late, while the ringing on the click screen spreads to both sides of the dashed line.

Reading the lab

The big screen sends one click through the EQ and draws what comes out, which is the filter's impulse response. Anything left of the dashed line came out before the sound that caused it. The bright shape is the mode you're hearing and the thin line is the other, so both are always on screen. Under it, the pink line is the curve measured from that click and the lane below shows how late each frequency comes out. The close-up screen next to it shows the loudest hit in the loop, with the 30 ms in front of it shaded, since that's where pre-ringing shows up. The Minimum phase and Linear phase buttons swap modes without touching the curve, so they're the switch to flip while you listen.

What does minimum phase EQ cost?

Its one cost is the phase shift, which collects around each change in the curve and grows when the change is steeper, bigger, narrower or lower in frequency. Here are the largest shifts the lab measures.

Low frequencies get the longest delays because their cycles are the longest; one cycle at 40 Hz lasts 25 ms. Even so, on a single sound you'll rarely hear any of it. The delayed frequencies are mostly the ones the EQ is already turning down, and your ears are far less fussy about timing between the frequencies inside one sound than about timing between two separate sounds. A minimum phase EQ rings too, but all of that ringing follows the sound, and a loud sound hides quieter ones that come straight after it.

The shift becomes a real problem when the EQ'd sound meets another copy of itself. Two copies that are out of step at some frequency partly cancel there, which is the same effect as a comb filter. Step 7 blends a 24 dB per octave high cut at 2.5 kHz half and half with the dry vocal. A clean blend would leave the top end a few decibels down, but at the cutoff the minimum phase copy is half a cycle behind the dry one, so the result dips 16.3 dB below where it should be, around 2.4 kHz.

What does linear phase EQ cost?

Latency

A linear phase filter is centred on the moment the sound arrives, so its first half has to play before that moment, and the only way to manage that is to hold the whole signal back by half the filter's length. The lab's filter is 8192 samples long. That puts everything 4096 samples late, which is 92.9 ms at 44.1 kHz. On playback your DAW's delay compensation hides it by holding back every other track to match, but while you're recording, or playing a synth through that channel, you'll hear each note late. The linear phase EQ lesson lists the latency for each common filter length.

Pre-ringing

Every sharp EQ change rings, and a linear phase EQ has to share that ringing evenly on both sides of the sound, so half of it plays before each hit. A loud sound covers quieter ones for a good while after it but only very briefly before it. Ringing in front of a kick therefore sits in the quiet gap, with nothing to hide behind, and you hear it as a soft swell or a smear leading into the transient.

Whether that's audible depends on where the ringing lands. The 100 Hz cut from step 2 rings 6.9 ms early on the click, but this loop has little energy there, so the 30 ms in front of the loudest kick stays 53 dB below the hit, the same as with no EQ. Step 3 moves the cut to 250 Hz at 48 dB per octave, into the body of the kick, and that gap rises to 35 dB below the hit, 18 dB louder than before. Step 4 switches the same cut back to minimum phase, and the front of the kick is clean again. You pay for it with 5.9 ms of shift around 240 Hz, which arrives after the hit, where it's covered.

CPU and low-end accuracy

Linear phase uses more processing, because one filter thousands of samples long is more work than the few small filters a minimum phase band needs. One on a master is nothing; one on every track of a big session adds up.

A filter of fixed length also runs out of room at very low frequencies, since it can't shape a frequency that only fits a few cycles inside it. Pick Bass in the lab, set a 48 dB per octave low cut at 40 Hz in linear phase, and the 8192-tap filter misses its curve by 5.8 dB at 29 Hz. Turn the Length knob up to 16384 taps and the miss shrinks to 2.6 dB, but the latency doubles to 185.8 ms. That's the trade the resolution or quality setting on a linear phase EQ makes for you.

When do the two sound the same?

Most of the time. Gentle, broad moves ring so little that the modes are close to identical. Steps 5 and 6 put a 3 dB cut at 400 Hz with a Q of 0.8 on the full loop. In minimum phase the biggest timing shift is 0.2 ms; in linear phase the click rings 1.2 ms early, 38 dB below the peak. Flip between the buttons with the loop running and listen for any change.

A 12 dB per octave high cut at 8 kHz on the same loop is gentler still, and the lab can't time any ringing for it in either mode. Most EQ work in a mix is made of moves like that, small amounts on wide bells and soft slopes. The phase mode starts to matter with steep filter slopes, narrow boosts, big gains and low frequencies, or when copies of a sound get blended.

Blending copies: where linear phase wins

Step 8 plays the vocal blend from step 7 in linear phase. Both copies share the same 92.9 ms delay, so they stay lined up and the result lands on the clean blend the mix knob asked for, with the 16.3 dB dip gone. Any time the EQ'd signal is added to another version of itself, this is the difference you're choosing between.

• Parallel EQ, through a mix knob set below 100% or a filtered copy on its own bus.
• Mid/side EQ, where the mid (what both channels share) and the side (the difference between them) get different moves. If the halves are shifted differently, they recombine slightly wrong and the stereo image moves around the frequencies you changed.
• One microphone of several on the same source, such as a close snare mic EQ'd against overheads that also hear the snare. The drum phase alignment lesson covers why those mics have to stay in step.
• Crossovers, where a multiband compressor splits a sound into bands and then adds them back together.

The same rule clears up a common worry. Two copies that go through the same minimum phase EQ shift together, so they stay in step with each other. The left and right channels of a stereo track with one EQ on it are fine, and so is a whole drum bus through one EQ. Trouble only starts when one copy is EQ'd and the other isn't, or the two are EQ'd differently.

Which phase mode for which job

How to choose between them, step by step

1. Start in minimum phaseIt's the default on nearly every EQ, including Ableton's EQ Eight, which has no linear phase mode at all.
2. Ask whether the sound gets blendedIf the EQ'd signal will be added to another copy of itself, through a mix knob, a parallel bus, mid/side processing or another microphone, switch to linear phase.
3. Check the low endIn linear phase, look for steep cuts or narrow boosts in the bass on anything with sharp hits. Solo the track and listen to the moment just before each kick. If it swells, soften the slope, widen the band or go back to minimum phase.
4. Keep it off the inputIf you're recording or playing through the channel, use minimum phase or bypass the EQ until the take is done.
5. Compare both modes and keep the cheaper oneFlip between them a few times while the track plays. If you can't hear a difference, keep minimum phase, since it costs nothing.

How to hear the difference with a null test

The lab plays one loop, but you can measure your own tracks in your DAW. Because the two modes draw the same curve, anything left over when you cancel one against the other is the difference in timing and nothing else.

1. Duplicate the trackMake sure your DAW's delay compensation is on, which it is by default in most.
2. Put the same EQ on both copiesUse the same plug-in and the same curve, minimum phase on one copy and linear phase on the other.
3. Flip the polarity of one copyUse a utility plug-in or the channel's phase invert button, then play both at the same fader level.
4. Listen to what's leftFor a gentle move it'll be close to silence. For a steep cut you'll hear a short burst near the cutoff frequency around each hit, which is the timing difference made audible.

Remember that the leftover is played on its own, with nothing to hide it. Something you can hear clearly in a null test can still be impossible to pick out in the mix, so treat it as a guide to where the modes differ and make the decision by ear on the real track.

Is there a mode in between?

Some EQs have one. FabFilter Pro-Q offers Natural Phase alongside its zero latency and linear phase modes; it aims to match the phase behaviour of an analogue EQ, with some latency but less than its linear phase settings need. Treat a mode like this as a minimum phase EQ for the questions on this page: it still shifts the frequencies around each change, so it won't blend cleanly with a dry copy the way linear phase does.

Common mistakes

Choosing linear phase because it sounds more accurate

The tone change is the same in both modes. Linear phase makes a different trade with timing, swapping a shift after each change for latency and ringing before it, and on a single track that trade is often impossible to hear. Choose it for a reason, like a blend, and judge it by ear.

Steep linear phase cuts on drums and bass

A 48 dB per octave low cut high enough to touch the body of a kick puts a swell in front of every hit, as step 3 shows. On drums and bass, a minimum phase cut is the safer choice, or a gentler slope if you need to stay in linear phase.

Mixing modes across copies

If you EQ a parallel bus or a close mic with a minimum phase EQ and leave the other copy dry, the cancellation from step 7 happens in your mix. Either use linear phase on the EQ'd copy or keep its moves gentle.

Tracking through a linear phase EQ

With tens of milliseconds of latency, often far more, a singer or player hears themselves late and the take suffers. Switch the EQ to minimum phase or bypass it while recording.

The curves themselves, and how to set them, are covered in the EQ lesson, and the phase lesson explains why two copies that are slightly out of step cancel.

Training your ears to tell them apart

The quiz under the lab plays the loop through a strong low cut or a narrow bass boost, in one mode or the other, with the screens covered, and asks which you heard. Linear phase gives itself away with a swell in the gap in front of each kick; minimum phase leaves the front clean and lets the low end hang on a touch longer after the hit. Your best score is saved in your browser.

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