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Author Topic: 2nd Order Minimum-Phase Filter?  (Read 5414 times)

Audio Craftsman

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2nd Order Minimum-Phase Filter?
« on: August 27, 2008, 06:47:06 pm »

(If this is the wrong forum for this question, please point me in the right direction.) In the June issue of Mix Bob Hodas wrote an artical about room tuning. I am trying to understand this:

"Learn which types of filters are used in the equalizer you’re going to apply to your system. It is important to understand room resonances and minimum-phase phenomena. This means that to truly correct a room resonance, you must use a second order minimum-phase filter. A linear-phase filter is good for correcting frequency linearity inside of a speaker box or perhaps to contour an instrument or voice in a track, but will not truly correct a room/speaker problem."

What is a second order minimum-phase filter?  Note: I do not have an electronics degree, so a "...For Dummies" answer would be appreciated.  Thanks.
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Andy Peters

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Re: 2nd Order Minimum-Phase Filter?
« Reply #1 on: August 28, 2008, 02:47:48 am »

Audio Craftsman wrote on Wed, 27 August 2008 15:47

What is a second order minimum-phase filter?  Note: I do not have an electronics degree, so a "...For Dummies" answer would be appreciated.  Thanks.


Put simply: ALL of your standard analog filters are minimum phase.

-a
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Tomas Danko

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Re: 2nd Order Minimum-Phase Filter?
« Reply #2 on: August 28, 2008, 03:41:04 am »

Second order would imply a +-12 dB boost/attenuate range.
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zmix

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Re: 2nd Order Minimum-Phase Filter?
« Reply #3 on: August 28, 2008, 09:30:04 am »

Tomas Danko wrote on Thu, 28 August 2008 03:41

Second order would imply a +-12 dB boost/attenuate range.



Tomas, that is not correct.  A second order filter has a slope of 12dB per octave, the filter's steepness has no bearing on the amount of cut and boost available.

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Re: 2nd Order Minimum-Phase Filter?
« Reply #4 on: August 28, 2008, 09:40:09 am »

zmix wrote on Thu, 28 August 2008 14:30

Tomas Danko wrote on Thu, 28 August 2008 03:41

Second order would imply a +-12 dB boost/attenuate range.



Tomas, that is not correct.  A second order filter has a slope of 12dB per octave, the filter's steepness has no bearing on the amount of cut and boost available.


Duh, sorry for that. Of course, it's the steepness per octave and nothing else. I should pay more attention when writing about poles in the middle of work.
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Jim Williams

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Re: 2nd Order Minimum-Phase Filter?
« Reply #5 on: August 28, 2008, 10:34:13 am »

Room "tuning" via 1/6 octave graphics was very popular back in the 80's. It would sort of work, if you placed your head in precisely the exact position of the measurement mics and if you didn't turn your head.  What I discovered watching room tuners is that if you moved the mics 2 inches, all the EQ settings would also be changed. That shows the futility of the method. They were trying to fix a time domain problem with a frequency fix. That would only work in a precise position as the time/frequency relationship constantly changes with position in the room.

Treat the room, not the monitors.
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Fletcher

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Re: 2nd Order Minimum-Phase Filter?
« Reply #6 on: August 28, 2008, 12:11:29 pm »

If you keep the measurement microphone in motion around the mix position and the response time of the analyzer at medium to slow you can get a good "average" for the mix position.

Our "average" area is about 3' wide and 2-2 1/2' tall from the center of the desk.  We use an Apex 1/3 octave graphic [on the 6db scale] which also has two bands of full parametrick EQ per side.

The shell is the shell is the shell... and nothing can fix that but architectural changes [and there is ALWYAS going to be compromises that need to be lived with in terms of any CR shell], but you can indeed tune the response of the drivers with EQ.  In my case, with JBL / UREI 813's there is an inherent "bark" to the compression driver in the 2.5kHz range which I can soften with the parametric EQ... and then kinda tune the rest of the response so I have the picture/curve I find pushes me in the directions I need to be pushed as a recording/mix engineer.

On the topic of filters... 6db per octave is considered a "first order" filter, 12db per octave a "second order" filter, 18db per octave 3rd... etc., etc., etc.

The more gentle the slope the less phase distortion you will encounter.

You can work in the digital domain with "phase linear equalizers" which manipulate code rather than manipulate the phase response [as occurs with analog filters]... but then you run into all kinds of agita with analog to digital and digital to analog conversion, clocking, etc., etc., etc.

I didn't read Bob's article but I was hanging with him on a Focal factory tour in the beginning of July.  One of the more interesting things I learned at Focal was that their drivers are built to "roll off" at frequencies very close to their cross over points which minimizes the need for steep filtering near the crossover point... which means that less "EQ" [crossover filter] is required which leads to a more even phase response from the multi-driver filled monitors.

I hope this description makes some sense...

Peace.
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CN Fletcher

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Re: 2nd Order Minimum-Phase Filter?
« Reply #7 on: August 28, 2008, 02:07:57 pm »

Thanks everyone.  Much appreciated.

The artical DOES mention averaging and moving the measurement mic around.  He also stresses the importance of speaker/listener placement first, before trying to apply EQ.

I generally prefer to work with acoustics before circuits.  And since we humans seem to be able to "listen past" some amount of acoustical and transducer anomalies, I don't find the trade offs of control room tuning worth the trouble, personally.

Mostly I needed to know that Minimum-Phase Filter means typical analog EQ as opposed to a digitally implemented Phase Linear EQ.  Interesting that he mentions second order, specifically.  Second order would NOT apply to a fully parametric filter, so I guess we have to assume he's talking about a graphic EQ, right?
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Andy Peters

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Re: 2nd Order Minimum-Phase Filter?
« Reply #8 on: August 28, 2008, 05:36:03 pm »

Audio Craftsman wrote on Thu, 28 August 2008 11:07


Mostly I needed to know that Minimum-Phase Filter means typical analog EQ as opposed to a digitally implemented Phase Linear EQ.  Interesting that he mentions second order, specifically.  Second order would NOT apply to a fully parametric filter, so I guess we have to assume he's talking about a graphic EQ, right?


You can certainly have a second-order fully parametric EQ. "Order" refers to the number of poles in the filter. The "parameters" of a parametric EQ are the gain, the center frequency and the width of the passband.

-a
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marcel

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Re: 2nd Order Minimum-Phase Filter?
« Reply #9 on: August 28, 2008, 05:59:19 pm »

Andy Peters wrote on Thu, 28 August 2008 14:36

The "parameters" of a parametric EQ are the gain, the center frequency and the width of the passband.

Isn't the width of the passband dependent on the filter slope?  It's just '2 slopes back to back', isn't it?
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MagnetoSound

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Re: 2nd Order Minimum-Phase Filter?
« Reply #10 on: August 28, 2008, 09:48:28 pm »

marcel wrote on Thu, 28 August 2008 22:59

Andy Peters wrote on Thu, 28 August 2008 14:36

The "parameters" of a parametric EQ are the gain, the center frequency and the width of the passband.

Isn't the width of the passband dependent on the filter slope?  It's just '2 slopes back to back', isn't it?



No, it's two different things. The area between the slopes is the passband.


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Re: 2nd Order Minimum-Phase Filter?
« Reply #11 on: September 02, 2008, 05:56:07 pm »

I think I explained this on another forum.  but i'll put it here.

Very briefly, and I am by no means an EE, so someone like Bruno will probably have a much better explaination/definition...  But the way I learned 10 years ago when I was in school was that...

All filters impart phase shift.  The name implies how they phase shift.

A linear phase shift is just that, the phase shift from 0 to 180 degrees is linear across the frequency spectrum.

A non-linear phase shift could be anything from an exponential curve across the spectrum or it could be wobby with a much more complex pattern.

A minimum phase shift is a filter that tries not to shift the phase at all... and so the curve will either look like a flat line with a few bumps/ripples in it or possibly flat across with a drop straight down to 180 degree shift (makes a right angle on the graph, no slope) in the middle, or a combination of both.

So, a digital linear-phase filter would not be useful for correcting room modes since you will be shifting the phase around the center frequency linearly, and would be pretty audible.

A minimum-phase filter would try to leave as much of the original signal intact and have the least amount of phase shift around the center frequency possible, which would (hopefully) be  less audible.

Again, I'm not an EE, nor do i claim to be any type of electric savvy person... i did take some classes in college a while ago and this is how I remember it.. which is to say, i could still be TOTALLY wrong... so please take this for what it's worth ($0.02).
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bruno putzeys

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Re: 2nd Order Minimum-Phase Filter?
« Reply #12 on: September 03, 2008, 03:18:47 am »

Tough job trying to find an easy to understand definition of all these things.

A first order filter is one of the following:
-a lowpass/highpass filter with a 6dB/octave slope
-a shelf
A second order filter is usually one of the following:
-a lowpass/highpass filter with a 12dB/octave slope
-a bandpass filter with 6dB/octave slopes on both sides
-a bell cut or boost
-any combination of two first-order filters

A minimum phase filter is one that produces the least possible amount of phase shift for a given amplitude response. Less phase shift than minimal implies that the filter would already be reacting to the input signal before it happened and that's clearly not possible.

A linear phase filter has a phase shift that's directly proportional to frequency (e.g. 0
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Fletcher

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Re: 2nd Order Minimum-Phase Filter?
« Reply #13 on: September 05, 2008, 10:57:48 am »

Bruno Putzeys wrote on Wed, 03 September 2008 03:18

A bell boost can be compensated exactly by a bell cut (of the same shape) with no phase shift whatsoever.


Wouldn't you experience the adverse effect of the phase shift created by any analog filter system... only twice?  

From what I understand [and I could certainly be wrong] the phase distortion created by the filter networks is constant whether you are applying the gain of the filtered region in positive or negative polarity.
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CN Fletcher

mwagener wrote on Sat, 11 September 2004 14:33
We are selling emotions, there are no emotions in a grid


"Recording engineers are an arrogant bunch.  
If you've spent most of your life with a few thousand dollars worth of musicians in the studio, making a decision every second and a half... and you and  they are going to have to live with it for the rest of your lives, you'll get pretty arrogant too.  It takes a certain amount of balls to do that... something around three"
Malcolm Chisholm

Andy Peters

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Re: 2nd Order Minimum-Phase Filter?
« Reply #14 on: September 05, 2008, 07:52:41 pm »

Fletcher wrote on Fri, 05 September 2008 07:57

Bruno Putzeys wrote on Wed, 03 September 2008 03:18

A bell boost can be compensated exactly by a bell cut (of the same shape) with no phase shift whatsoever.


Wouldn't you experience the adverse effect of the phase shift created by any analog filter system... only twice?  

From what I understand [and I could certainly be wrong] the phase distortion created by the filter networks is constant whether you are applying the gain of the filtered region in positive or negative polarity.


I suppose we should point out that the phase shift caused by filters is not phase distortion and is not "adverse." You simply wouldn't have filtering (in the analog domain) without phase shift.

Bruno's point is that a minimum-phase filter has a conjugate (that is also minimum-phase) that can completely undo the effects of the first. The phase shift caused by the boost filter goes "in one direction" and the phase shift caused by the equivalent cut filter (same bandwidth, cut amount is equal to the boost amount) goes "in the other direction" so the resulting phase shift (and gain) is zero. You are literally "undoing" the filter in both phase and amplitude.

This is why minimum-phase networks are so useful. If you know that your anomaly is in fact minimum phase, you can design a reciprocal network to fix the problem.

-a

-a
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