The difference between minimum-phase and linear-phase EQ on transient signals such as snare drum
On the topic of filters and EQ, the terms 'minimum phase' and 'linear phase' are often seen, but not so often well-understood. Or well-explained for that matter. But I'm going to have a go at demonstrating one aspect of the difference between minimum phase and linear phase EQ. But first, my attempt at an explanation...
As you know, EQ changes the level balance of frequencies in a signal. So you can boost or cut the bass, cut or boost the high frequencies, play with the mids etc. until you have achieved the 'perfect sound'.
Of course, you would have made more progress towards the perfect sound by experimenting more with your mic position during the session, but we'll let that pass for now.
As a side-effect of changing the level balance of different bands of frequencies, conventional EQ also changes their phase relationships. So low frequencies can be delayed with respect to high, or vice versa, depending on how the EQ parameters are set. We call this 'phase shift'.
'Minimum phase' means that the amount of phase shift that happens is as little as possible. In a simple electronic circuit, or its algorithmic equivalent, this is what should happen. It is possible to design a circuit or algorithm with more than the minimum phase shift, but this would only be done if the extra phase shift was actually wanted, such as in the all-pass filter which only affects phase and not the level balance of frequencies.
Having no phase shift is good?
It's easy to see why it would be nice not to have phase shift in a filter or EQ. The timing relationship of the various frequencies would be the same at the output as they were at the input. And who would want these time relationships messed up?
The expression 'transient smearing' is sometimes used, meaning that when there is a sudden attack in the signal, such as a kick or snare drum, then since different frequencies will be delayed by different amounts, then the transient will not attack in the same way as it did before filtering or EQ. As we shall see in a moment, applying the expression 'transient smearing' to minimum phase filters and EQ can be rather misleading.
To summarize so far, the minimum phase filter or EQ changes the phase, or timing, relationship between the frequency components of the signal as well as the frequency balance.
Since the linear phase filter or EQ does not create any phase shifts, it must be better, right? Yes, there are situations where this is a definite advantage. But this does not mean that there are no negative consequences.
As always in life, there is no free lunch. Linear phase filters and equalizers have the unfortunate side effect of creating audible 'pre-ringing' in some types of signal, such as the attack of a snare drum.
I have a snare drum recording right here...
As much as I like this sound just as it is, I'm sure I can make it more interesting with EQ. So I'll insert the FabFilter Pro-Q 2 plug-in, which can provide both minimum phase and linear phase EQ. When I say I'm going to make the sound more interesting, I mean more interesting for this example. My EQ might be a little too extreme for normal musical use, but it will serve to help make my point.
Here is my EQed version, with the minimum phase setting (which FabFilter calls 'natural phase' because it "closely matches the analog phase response", possibly because it isn't quite perfectly minimum phase, but it will make no practical difference here)...
By cutting the lower frequencies significantly with a steep slope and a high Q I have asked the EQ to do a lot in terms of changing the signal. That allows us to hear any problems clearly. But there seem to none. Only the frequency balance is changed as expected.
Now lets click over to linear phase mode, at the Pro-Q's highest quality setting...
Wow, that's different! Hear how the lower frequencies swoop up in level before the actual attack of the drum. It doesn't sound right at all. This effect is known as 'pre-ringing' because it anticipates the signal. (There is no time travel necessary because the output of the signal as a whole is delayed while the plug-in does its processing. This delay is another potential problem of linear phase filters and EQ.)
Is this bad?
It would be better to think of this effect as different rather than bad, because this demonstration is intended to make the pre-ringing effect obvious. You might even prefer the sound of pre-ringing in this example. You might think that this isn't such a big deal and in real life usage no normal listener would notice. Well that's probably true, but it is also true that a lot of ill-judged small differences can add up to an end-product that is unmarketable. It is the producer's or engineer's duty to listen to a higher level of precision than their client or purchaser and make sure that every tiny detail of their work is as good as it can possibly be, within practical limits.
At this point I need to return to the accusations made of minimum phase filters and EQ that they are guilty of transient smearing. Well yes they are, but I would say that transient smearing, even at its worst, isn't nearly so significant a defect as pre-ringing on percussive sounds.
Now that you have heard the effects of pre-ringing in linear phase EQ, lets try a slightly more realistic example. Here is a clip of drums processed through the FabFilter Pro-Q 2 with the minimum phase setting...
And the same clip with the same EQ, but set to linear phase...
I'll leave it to you to judge the differences and whether you like what you hear.
This is just one aspect of the difference between minimum phase filters and EQ and their linear phase counterparts. Linear phase has advantages in other areas, but the side effect of pre-ringing must always be considered.