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linear phase versus minimum phase (EQ's)
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bryan k
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11th January 2011
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linear phase versus minimum phase (EQ's)

What exactly is the difference between "linear phase" and "minimum phase" when talking about EQ's?

Is there a preference for one over the other when dealing with specific tasks?

Sorry, for such a Noob question.......but for a General mastering EQ, I hear so many different EQ styles/brands recommended, and "linear phase" this...."linear phase" that....comes up alot when asking about a mastering EQ.

Yet plugins such as Flux Epure (which is NOT a linear phase EQ) gets such rave reviews for a mastering EQ.

So whats the deal? Whats the difference between "linear phase" and "minimal phase"?
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The two most basic categories of digital filters are FIR and IIR. An analog filter will be IIR, while a digital filter can be either FIR or IIR. FIR stands for Finite Impulse Response, and typically, though not necessarily, these will exhibit a linear phase response. This means that as all frequencies propagate through the filter, they will arrive at the output at the same time. Finite Impulse Response means that the filter’s response to an impulse will settle to zero in a finite time.

IIR stands for Infinite Impulse Response, which will be minimum phase (dual pass IIR to achieve linear phase being an interesting exception), and though the total delay might be less than FIR filters, some groups of frequencies may be delayed more or less than others (i.e. group delay). An IIR filter’s response to an impulse may last indefinitely due to feedback in the filter.

Both linear phase FIR and minimum phase IIR filters exhibit phase distortion. The difference is that the distortion is linear in one, and non-linear in the other. The linear phase filter introduces the same delay at all frequencies. The more aggressive the filter, the greater the latency through the filter. You can make an almost infinitely steep FIR filter, but you may have to wait until next month to hear the output. The pre-echo (often called pre-ringing) is the other obvious drawback. Post-ringing in IIR filters (and FIR) is less of a problem since it is typically masked by the signal.

For practical purposes, despite what plugin advertisements may lead you to believe, much of the typical use of EQ in mastering is well-accomplished with IIR as it is correcting for minimum phase problems. Linear phase filters used for high-pass or other low frequency applications can come at the cost of conspicuous ringing. On the other hand, linear phase filters are at home in low-pass applications in AD/DA converters.
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Yep the drawback of any kind of eq...
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Wow, thanks for the detailed explanation. I'm still digesting it....

So for low/high shelf boosting/cutting......one should use the "minimal phase" type? What If your doing normal bell curve or wide Q cutting/boosting, should one use linear phase? Or would minimal phase EQ be a better option yet again?
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No opinion. Let your ears decide?
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Great reply Jay, thanks for contributing solid info!
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Quote:
Originally Posted by jayfrigo View Post
The pre-echo (often called pre-ringing) is the other obvious drawback. Post-ringing in IIR filters (and FIR) is less of a problem since it is typically masked by the signal.
Yep. That's a deal-killer for me too.

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much of the typical use of EQ in mastering is well-accomplished with IIR as it is correcting for minimum phase problems.
Exactly. Minimum Phase is what occurs in nature with ringing, and peaks and nulls, and proximity effect etc. So these are best countered with the same type of filter in reverse.

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bryan k
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ok, so it sounds like minimum phase is the choice to go with......

But then why are so many manufacturers making so-called "mastering EQs" hyping the fact they are linear phase, if in fact linear phase is not the best choice for this type of application?
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Quote:
Originally Posted by bryan k View Post
ok, so it sounds like minimum phase is the choice to go with......

But then why are so many manufacturers making so-called "mastering EQs" hyping the fact they are linear phase, if in fact linear phase is not the best choice for this type of application?
1. Who wants an EQ called "Minimum" when it could be "Linear?"
2. The Internet
3. ?


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bryan k
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damn, im glad I learned about this.....and not fall into the Hype.

I was curious about Flux Epure (i guess is a minimum phase) and Sonaris Mastering EQ (apparently has both capabilities of either linear or minimum phase per band)........

I knew Flux was raved about being this Great EQ for mastering, but i never understood why because it wasnt classified as a "linear phase", even though the Hype at the time was saying linear phase was the way to go.

price point, Sonaris mastering EQ and Flux are the same....yet Sonaris gives you the option of choosing a phase type.....

Which would be the way to go in your guys opinion?
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Quote:
Originally Posted by jayfrigo View Post
The two most basic categories of digital filters are FIR and IIR. An analog filter will be IIR, while a digital filter can be either FIR or IIR. FIR stands for Finite Impulse Response, and typically, though not necessarily, these will exhibit a linear phase response. This means that as all frequencies propagate through the filter, they will arrive at the output at the same time. Finite Impulse Response means that the filter’s response to an impulse will settle to zero in a finite time.

IIR stands for Infinite Impulse Response, which will be minimum phase (dual pass IIR to achieve linear phase being an interesting exception), and though the total delay might be less than FIR filters, some groups of frequencies may be delayed more or less than others (i.e. group delay). An IIR filter’s response to an impulse may last indefinitely due to feedback in the filter.

Both linear phase FIR and minimum phase IIR filters exhibit phase distortion. The difference is that the distortion is linear in one, and non-linear in the other. The linear phase filter introduces the same delay at all frequencies. The more aggressive the filter, the greater the latency through the filter. You can make an almost infinitely steep FIR filter, but you may have to wait until next month to hear the output. The pre-echo (often called pre-ringing) is the other obvious drawback. Post-ringing in IIR filters (and FIR) is less of a problem since it is typically masked by the signal.

For practical purposes, despite what plugin advertisements may lead you to believe, much of the typical use of EQ in mastering is well-accomplished with IIR as it is correcting for minimum phase problems. Linear phase filters used for high-pass or other low frequency applications can come at the cost of conspicuous ringing. On the other hand, linear phase filters are at home in low-pass applications in AD/DA converters.
Great explanation, will be quoting/sharing.
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13th January 2011
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UAD product "precision mastering EQ" is IIR, is this evidence of Universal Audio showing more integrity than software houses that jump on the "linear phase" bandwagon?

It's great to get some practical experience of what works alongside the signal processing theory, thanks for sharing knowledge all.
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interesting...i was readin up on the Sonoris Mastering EQ, and this is what they had to say about it....

Quote:
The linear phase algorithm of the SMEQ is based on a technique called “backward-forward filtering”, until now only implemented in some expensive high end equalizers. The main advantage of this technique is that IIR filters can be used instead of FIR filters, the latter is commonly found in linear phase implementations. IIR filters are known for their more analog kind of filtering and are also more efficient than FIR filters.
So apparently, they have a linear phase EQ that uses IIR filters....

sounds like its the best of both worlds......
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Quote:
Originally Posted by bryan k View Post
interesting...i was readin up on the Sonoris Mastering EQ, and this is what they had to say about it....

So apparently, they have a linear phase EQ that uses IIR filters....

sounds like its the best of both worlds......
That technique still has all the pre-ringing of FIR, but has some advantages in implementation.


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Quote:
Originally Posted by bryan k View Post
interesting...i was readin up on the Sonoris Mastering EQ, and this is what they had to say about it....



So apparently, they have a linear phase EQ that uses IIR filters....

sounds like its the best of both worlds......
I've been using both Flux and Sonoris. Both eq's have excellent flexibility for m/s and the sonoris for reasons you posted and more is even more flexible. Personally i find the Flux HP and LP filters to be smoother than the Sonoris, but for overall Eq the Sonoris on a Master Bus or Mastering is a wee bit more transparent sounding. I can get a little more lift without hearing the eq so to speak. I use the Flux quite a bit for mixing eq duties more so than the Sonoris due to CPU hogging. Both are excellent, but for mastering i would lean with Sonoris, that's what my ears tell me.
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Quote:
Originally Posted by dcollins View Post
That technique still has all the pre-ringing of FIR, but has some advantages in implementation.


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Shit.....down the rabbit hole i go again........

so even though the sonoris linear phase has IIR filters, its best just to use the minimum phase cause its the same IIR filters, but without pre-ringing...

is this correct?
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Shit.....down the rabbit hole i go again........

so even though the sonoris linear phase has IIR filters, its best just to use the minimum phase cause its the same IIR filters, but without pre-ringing...

is this correct?
If it's linear phase, it has pre-ringing. There is no way around it.


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Dave's quite right. Analogue linear-phase filters (most notably the class of filters first described by Lerner in the 1960s and which bear his name) are IIR and have pre-ringing. The audibility of pre-ringing is of course deeply variable depending on the frequency, the stimulus and the sharpness of the filter (and hence the length of its associated pre-ringing) and it isn't always a problem in practice, but it pays to be cautious. Some DSP implementations have longer pre-ringing than one might expect from basic principles.
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Quote:
Originally Posted by bryan k View Post
So apparently, they have a linear phase EQ that uses IIR filters....
Yes, this is what I referred to in the parentheses when I said:

Quote:
IIR stands for Infinite Impulse Response, which will be minimum phase (dual pass IIR to achieve linear phase being an interesting exception)
To simply it, it's basically sending it through a second time in reverse to correct for the phase. Whereas post-ringing after the impulse in a regular IIR is less noticeable because it is masked by the signal, in a non-causal (the cause does not precede result) or FIR filter you get ringing (pre-echo) before the transient. When you use the second pass of IIR in reverse to correct the phase, your post-ring is now a pre-ring when you listen to your resulting filtered signal.

As Dave points out, no free lunch.
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Originally Posted by jayfrigo View Post
Both linear phase FIR and minimum phase IIR filters exhibit phase distortion. The difference is that the distortion is linear in one, and non-linear in the other.
What's the difference between "phase distortion" and "phase shift" when referring to the phase response of a minimum phase IIR filter? I see the terms used seemingly synonymously sometimes, and other times both terms are used separately which implies a distinction.
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I realize the following company is selling its product but it offers insight to what it claims to be the benefits
of linear phase. It goes beyond the "pre-ringing" focus of this thread thus far. What's interesting is it claims
not to just be more 'transparent' and 'natural', it says it preserves transients in a better way. Any thoughts
on that case they make for its use? NuGen Audio - Professional Audio Software - SEQ Mix and Mastering EQ
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Originally Posted by timlloyd View Post
What's the difference between "phase distortion" and "phase shift"
Technically, "distortion" is any change. So you could use either term and not be wrong. However, I reserve the term "distortion" for situations where there's non-linearity. Phase shift is linear, so I prefer not to call it distortion. But that's just me.

--Ethan
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Sometimes our first impression is to think of the term distortion as meaning things that get fuzzy, but that's only one kind of distortion. Phase is time, so to change the natural time relationship is to distort the phase. If the change is equal at all frequencies, it is linear; if it is different for certain frequencies, it is non-linear, aka group delay, meaning certain groups of frequencies are delayed as compared to other groups. A minimum phase relationship ties together phase and magnitude.
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Originally Posted by Ethan Winer View Post
Technically, "distortion" is any change. So you could use either term and not be wrong. However, I reserve the term "distortion" for situations where there's non-linearity. Phase shift is linear, so I prefer not to call it distortion. But that's just me.
Yeah that's how I define distortion as well - non-linearity.

Quote:
Originally Posted by jayfrigo View Post
Sometimes our first impression is to think of the term distortion as meaning things that get fuzzy, but that's only one kind of distortion. Phase is time, so to change the natural time relationship is to distort the phase. If the change is equal at all frequencies, it is linear; if it is different for certain frequencies, it is non-linear, aka group delay, meaning certain groups of frequencies are delayed as compared to other groups. A minimum phase relationship ties together phase and magnitude.
This is what I thought. So you're both saying that in the case of a minimum phase system, "phase shift" and "phase distortion" are referring to the same aspect of the system? This makes perfect sense to me. However I've conversed with people who say that in such systems they are different, and that they both happen. Even that while the "amount of phase shift" in an equivalent cut and boost curve is the same (but of opposite "polarity" around 0 degrees), the "phase distortion" will differ......which hearkens back to the "cut before boost" debate (I don't want to go into that discussion here - I already know the reasons for this guideline and when to disregard it).

I'm just trying to get the concepts straightened out in my mind for pedantic reasons

Thanks
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Quote:
Originally Posted by timlloyd View Post
This is what I thought. So you're both saying that in the case of a minimum phase system, "phase shift" and "phase distortion" are referring to the same aspect of the system? This makes perfect sense to me.
It just means that the phase is not constant with frequency, as it is with FIR.

Quote:
However I've conversed with people who say that in such systems they are different, and that they both happen. Even that while the "amount of phase shift" in an equivalent cut and boost curve is the same (but of opposite "polarity" around 0 degrees), the "phase distortion" will differ......which hearkens back to the "cut before boost" debate (I don't want to go into that discussion here - I already know the reasons for this guideline and when to disregard it).
One of the properties of minimum phase is that the phase shift is completely controlled by the amount of boost/cut and the Q. This means that if you add a dB at 100Hz and then cut a dB, the net phase shift is zero.

This also means that any two IIR or analog eq's that have the same curve also have exactly the same phase shift.

One of the many weird aspects of FIR eq is that in theory you can't exactly reverse the eq the way you can in IIR or analog.


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Originally Posted by dcollins View Post
One of the properties of minimum phase is that the phase shift is completely controlled by the amount of boost/cut and the Q....

This also means that any two IIR or analog eq's that have the same curve also have exactly the same phase shift.
This is exactly what I thought! Thanks for confirming.
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This is a fascinating thread! Thanks all who are participating.

I've never really known the technical details here - but I have found the waves lineq to be a fantastic choice for vocals. I have expected it to be good on 2-buss processing, but have always felt that it lacks the transparency I seem to get when using it on unique sources. I've always found this to be weird - but now I understand why I keep using minimal phase eqs on the 2-buss. Because I'm not generally making large cuts or boosts, so the distortion is very subtle on the minimal phase eqs, perhaps they are overall more transparent for this purpose.
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Originally Posted by dcollins View Post
One of the many weird aspects of FIR eq is that in theory you can't exactly reverse the eq the way you can in IIR or analog.
Why is that? Since most FIR EQs are linear phase, adding 1 dB after cutting 1 dB will get you back to the original. No need to equalize the phase response because there was no change to the phase response.
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'Phase shift' and 'phase distortion' are generally used for the same thing: frequency-dependent time delay.Technically, phase shift also includes frequency-INdependent time delay, but for audio purposes that is generally trivial (hey, the audio has already been delayed by several days, months or years!). The word 'distortion' is most often used by people who are trying to sell you systems that don't exhibit it.

Note that there are filters whose response is neither minimum- nor linear-phase. The most obvious example of this is a system consisting of a minimum-phase filter followed by a linear-phase one. What's more, all three structures (minimum, non-minimum and linear) can be realised in either analogue or digital domain, and in the latter case with IIR or FIR characteristics (with the one exception that you can't make a true minimum-phase FIR filter, though you can make a close approximation). So you have to be a bit careful about terminology. Yes, the vast majority of analogue and IIR filters are min phase, and the vast majority off FIR are lin phase, but there is no synonimity.
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