Question about minimum phase resonance and corrective EQ

[moosa17]

Hi, I wasn't sure what subforum to post this in, but I think it's perhaps most appropriate to ask here, since I think it's at least related to DSP concepts.

I've been doing some reading on room acoustics and treatment as well as corrective EQ, and I came across an interesting claim. The source of the claim is in the following paper, at the bottom of the 7th page: http://old.infinitysystems.com/home/tec ... design.pdf

Room resonances at low frequencies behave as “minimum phase” phenomena, and so, if the amplitude vs. frequency characteristic is corrected, so also will the phase vs. frequency characteristic. If both amplitude and phase responses are fixed, then it must be true that the transient response must be fixed – i.e. the ringing, or overhang, must be eliminated.

So the claim, if I understand it, seems to be that correcting a resonant peak with EQ will not only attenuate it and the ringing but actually remove the ringing altogether.

There's also an article here which includes some real-world measurements which may corroborate that claim: http://www.acousticfrontiers.com/201163 ... odes-html/

I'm wondering if someone might be able to further explain this in a way that I can understand it better. My understanding has been that corrective EQ can only correct frequency domain distortions and not time domain distortions, but if this is true it would be a significant exception.

So my questions, if anyone might be able to answer them, are:
How does a "minimum phase" resonance ring or not ring based on the relative (not absolute) amplitude of that particular frequency?
How does a room's lower frequency resonance end up behaving as "minimum phase?"

Thanks for your time.

[camsr]

The error is phase is smaller with lower order room modes. But it's not minimum phase.

[JCJR]

Hi Moosa17

I do not understand acoustics very good, but one reference which might be a good starting point--

http://www.roomeqwizard.com/

Room EQ Wizard is an excellent, mature, free (donation-ware) acoustic analysis program. The documentation is excellent (available under the HELP tab on the website). The author John Mulcahy is a sharp fella who has worked in acoustics for many years. Not only smart but also a very nice fella.

The documentation has some explanations about minimum phase in room responses. The REW software has options which can take a room sweep and unwrap the phase to plot phase error versus frequency. I may be using slightly improper terminology.

Anyway, you can get a frequency vs phase plot, where the phase plot shows the deviation from minimum phase. According to the author, there are good odds of successful EQ on frequencies which are fairly close to minimum phase response.

However, odds are poor that EQ will help on frequencies showing large deviation from minimum phase. A fool's errand attempting to EQ non-minimum-phase frequencies. If you try to boost a null, the room will eat-up, cancel-out, about any amount of power you pump into the room. It won't fix the null and makes frequencies in vicinity of the null perform worse.

Peaks are easier to notch out. OTOH even notch filters, so far as I know, need impulse responses equally long as a same-frequency boost filter. But notch filters do seem somewhat "anti-resonant" even though they need rather long impulse responses at bass frequencies. I don't understand it very well, as can easily be seen.

Heavy room treatment can help straighten out the bass phase response. After I treated my small room as heroically possible, was able to slightly improve the final response by modestly notching a couple of bass peaks. But even after fairly heavy bass trapping, the worst bass null, in the REW minimum phase plot, just coincidentally is the only part of the plot which shows large deviation from minimum phase. So I can fix the frequencies that ain't broke, but can't EQ-fix the frequency that IS BROKE!

Sometimes multiple subwoofers can help, though room treatment as heavy as you can afford would be the first thing to do, before even firing up an equalizer.

[moosa17]

Thanks for the responses. I've had a brief look at that doc you brought to attention JCJR and found this seemingly relevant bit:

Minimum phase systems can be inverted, which means that a filter can be designed that, if applied to the system, would produce a flat response and correct the phase response at the same time.

I simply don't have much of an understanding of filters or "minimum phase systems" beyond the practical applications in music. So I think I can't fully appreciate the meaning here but it is starting to make a little more sense. I mean, at least the idea that if a minimum phase system is invertible by definition then it should be possible to negate it and its ringing effect. So somehow an inverted filter is created that nullifies when combined with the effect within the room, that behaves like a minimum phase filter. Still seems strange to me that something in the time domain could be so readily inverted.

Probably if I had any proper DSP education this would make a lot more sense.

[JCJR]

Hi moosa17

One thing to consider, so far as I know most properly made analog music EQ's, or IIR digital music EQ's, behave in a minimum phase fashion. So if a room rings at Frequency X, the room acting like a mechanical EQ boost at frequency X-- If that room mechanical EQ response is near minimum phase, then you ought to be able to straighten out the frequency response with a cut on a minimum phase EQ device. If it is a peak at frequency X and width Y, then an EQ notch at frequency X and width Y ought to be able to flatten it out a good bit.

However I don't think ordinary EQ would reduce the room decay time. Depends on what you consider as "evidence".

For instance you look at a room waterfall plot and there is a big peak at 100 Hz. Also the waterfall plot shows an excessively long room decay tail at 100 Hz--

For instance, RT60 is the time it takes for audio to decay -60 dB. If that big old 12 dB peak at 100 Hz takes 1 second to decay to the average -60 dB level, then if you notch the peak out by a -12 dB eqqualizer cut, then the waterfall plot will show a shorter 100 Hz decay tail, merely because you didn't pump so much energy into the room at 100 Hz. But the room still has a resonant problem, a too-long 100 Hz decay, regardless that we just turned down the drive at the problem resonant frequency.

OTOH if that problem 100 Hz room resonance is not near minimum phase, so far as I know, ordinary EQ probably won't help much or at all.

Do you know causal versus non-causal? Causal is what usually happens in the real world. You do something, and then later in time something else happens in response. Cause always precedes effect. That is how analog filters and "causal" digital filters work. You never get a signal coming out, until after you send a signal in.

Using short delays, digital filters can be made non-causal. In effect, you start getting signal out before you send signal in. For a few decades, some folks have worked on fixing room problems by inverting the time response of the signal you feed thru the speakers. For instance if there are reflections coming back from the room, you can send low-level advanced or retarded copies of the music to cancel out the reflections like they never happened.

I suppose you could call this a case of extreme EQ, but I think the most common buzzword is DRC-- Digital Room Correction if you wish to google it.

Supposedly it really is feasible to almost completely cancel out a bad, untreated room response. But only at one special place in the room. Some softwares can make it great, as long as you never move your head from that special place where you put the measurement mic when you set-up the software. Every other place in the room will probably sound worse from such extreme correction.

The big DRC products deal with this by requiring measurements from multiple locations, moving the mic over a pre-determined grid of locations and doing the test at each location. Then the software tries to come up with a combination of pre-echoes and post-echoes that will fix the room as good as possible, on average over the area covered by the multiple mic measurements. Hopefully it improves the sound over a wider sweet spot, but the tradeoff is that there will be less improvement than if you could correct for only one tiny listening position in the room.

Some companies selling DRC almost imply that it is good enough that you don't need room treatment. So maybe it can improve an untreated room, but will probably work even more gooder if you treat the room as good as possible before installing the DRC.

I haven't tried DRC. Got the room treated "fairly good" and then modest settings on an ordinary EQ makes it "a little better" than no EQ at all.

[moosa17]

However I don't think ordinary EQ would reduce the room decay time. Depends on what you consider as "evidence".

This was my understanding as well, however what I'm reading suggests that this is true with one exception, which is this "ringing" phenomenon. Other reverberations are not affected by this.

For instance, RT60 is the time it takes for audio to decay -60 dB. If that big old 12 dB peak at 100 Hz takes 1 second to decay to the average -60 dB level, then if you notch the peak out by a -12 dB eqqualizer cut, then the waterfall plot will show a shorter 100 Hz decay tail, merely because you didn't pump so much energy into the room at 100 Hz. But the room still has a resonant problem, a too-long 100 Hz decay, regardless that we just turned down the drive at the problem resonant frequency.

Indeed, this is also something that occurred to me, but again the claim as it's written is that the ringing can actually be nullified to some extent, not just attenuated. In the second link I posted above, which contains some measurements and graphs, there are a couple graphs that were said to be amplitude normalized in response to this very idea, and they did appear to show a significant improvement in the time-domain response.

Funny thing, I've heard about room deconvolution from someone in the past and I basically decided it was bullcrap, saying something to the effect that once the sound leaves your speakers you have no further control over it. But after reading your little explanation of it I realized that does make sense after all, haha. I'm not sure whether that is the same or related to this or not though.

To be clear, I'm just interested in understanding this at this point, not actually intending to put any corrective EQ into practice. It was just something that challenged my previous assumptions and so I wanted to understand it better.

[JCJR]

Hi moosa17

The fellas who appear to actually know something about acoustics, admit that it is a non-intuitive field. Acoustics can behave in ways that the average fella would not consider "common sensible". Made worse because there is so much BS in acoustics, masquerading as expertise.

There are big fat introductory books on acoustics, with a few simple formulas and hundreds of pages practical advice. Then below that level comes the physics of acoustics which might seem simple to a young bright physics student, but the math hurts my brain.

Awhile back got the idea maybe it would be possible to design absorbers with a known amount of phase shift. Fiber-based absorbers act kinda likee lowpass filters and they all have some amount of phase shift which can be measured easy enough. Was wondering if it might be possible to design-in a prescribed phase shift. Anyway the math got to deep for me.

Asking a couple of acousticians, got the impression maybe they don't fool with that. Nobody answered my question how it would be done anyway. Just saying, if you ask an electronic engineer how to design a filter with a specified phase shift, he won't have any problem telling you how to do it. Easy-peasy for an expert professional EE.

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The author of that paper, Floyd E. Toole PhD-- So far as I know he is highly-regarded among his peers. The odds might be purt good that he is not peddling BS. Though it might be possible to read his claims and misunderstand in one way or the other. His work seems more focused on "listening rooms for the masses" rather than studio control room design, so far as I know. OTOH residential listening rooms vastly outnumber recording studios and might be the "more important" market subset.

I didn't read his entire paper yet, but in the section you pointed out, he mentions that he did not try to correct bass nulls in the test room. And in another paragraph warns that trying to EQ nulls is a fool's errand.

[JCJR]

The idea that a pair of stereo speakers can be processed to un-do room problems, seems the hardest for me to believe. But there has been more credible work using multiple speakers to "un-do" room problems.

There has been some work using big cheap subwoofers as tunable bass traps, instead of installing big fiberglass absorbers or helmholtz absorbers. Basic idea, you build big sealed speaker boxes with cheap-ass 18" speakers. Not connected to an amp. Then by connecting a passive network of resistors, inductors and capacitors to the speaker voice coil, you can tune the speaker's damping. If pyle 18" speakers would work good enough, then maybe it wouldn't cost much more than a big dumb box full of fiberglass, and would be tunable.

Just thinking, ordinary monitor speakers in a room, motion-controlled by the high damping of the amplifier, might have at least a small amount of bass trapping capability just by being in the room. A monitor speaker with big woofers probably better at this than a monitor speaker with tiny woofers.

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There has been work on "active bass traps"-- You build decent subwoofers and put them in room corners, where you would ordinarily install bass traps. You drive the subs with the delayed inverse of the audio which arrives at the corners. So the relatively small sub can actively cancel out a bunch of bass, behaving like a much bigger passive bass trap.

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It may have been Mr Toole, or some other academic, who mentioned that rooms with surround systems already have speakers all over the room, so maybe they could be driven with conditioned signals so that the surround speakers are both speakers and active bass traps at the same time.

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There are several other interesting multiple speaker active correction schemes which do work, though some of them require quite a bit of custom building and a big budget for lots of speakers.

[JCJR]

For my small room bass null, I tried crude active bass trap-- A second subwoofer in a back corner, driven by a delayed equalized inverted signal, and it did work fairly well. Then after a few months the old quadraverb I was using to drive the rear sub, died.

So another set of papers I had not really believed, claimed that merely placing several subwoofers in different places in the room, with EQ and level tweaks, tends to reduce bass null problems. The nulls in the room from subwoofer A get filled in with peaks from subwoofer B and vice-versa.

So after the quadraverb died, I just drove the remote sub with a tweaked non-delayed signal, and it worked about as effectively as the fancier "active bass trap" approach. Though a properly installed and tweaked "active bass trap" system might be able to shorten the room time response errors. Multiple subs just level out the bass frequency response, but so far a I know can't shorten the room's impulse response.

It flattens the small room frequency response pretty good, but doesn't make the room's low frequency time response problems go away. Low bass control needs rather heroic room treatment so far as I can tell.

With treatment, mild EQ, and the dual subs, got to these frequency response stats--

Max/Min Deviation (from Mean SPL) = +2.837 / -4.23 dB
Mean Absolute Deviation = 0.89943 dB
Median Absolute Deviation = 0.75202 dB
90th Percentile Absolute Deviation = 1.866 dB
99th Percentile Absolute Deviation = 2.767 dB

In the spectrogram, time goes from bottom to top, frequency from left to right. Everything that is red is within a window of about 4 dB.

That jink in the response at the crosshairs, near 40 Hz. Without the second sub it was a rather deep null. The second sub helped fill the frequency response null, but the room impulse response down there is still quite dodgy. Was much worse before treatment.

REW displays the area of that jink as the largest deviation from minimum phase.

[moosa17]

JCJR, thanks for taking the time. I need to continue reading about room acoustics. Like you I loathe the math, just skip over it really, but the practical applications of stuff is really interesting. Even some of the relatively straightforward concepts, it seems like very few people are aware of it at all, so it feels a bit like discovering something new.

The idea of using dead subwoofers as absorbers is hilarious. In my brief reading so far I've come across the concept of "membrane absorbers," which I think is about the same thing. Low frequencies move the membrane like a diaphragm and it absorbs around a particular resonant frequency. Supposedly much more efficient handling bass frequencies and below than fiberglass, which you'd need to go a foot thick before you start to get down to those lower Hz.

[hugoderwolf]

It is definitely possible to alter room mode decay times using filters. But it's a good idea to throw away the magnitude approach altogether for that. Think of every resonance as a pole pair in z-Plane. Place a filter that has a zero where the pole is and it's gone. The hard part is figuring out where exactly the zero must be and how to prevent the compensation filter from doing all too nasty things to the magnitude response. But there are solutions for that.

There are however some problems left for that to really work. These mainly have to do with the speaker and listener positions and thus the coupling of the speakers to the room.

[moosa17]

Hi hugoderwolf. Thanks for offering your explanation.

It's a little over my uneducated head (I'm just a musician really; who has time for real school?), but I can understand how it could not be a matter of simply adjusting magnitude.

I think primarily I was looking for some reassurance that this idea I was reading about was founded in reality, and also that it was being presented accurately. Some of what I like to do is share things I've learned with other people, so at the least I do my best not to mislead anyone.

[kippertoffee]

It is definitely possible to alter room mode decay times using filters. But it's a good idea to throw away the magnitude approach altogether for that. Think of every resonance as a pole pair in z-Plane. Place a filter that has a zero where the pole is and it's gone. The hard part is figuring out where exactly the zero must be and how to prevent the compensation filter from doing all too nasty things to the magnitude response. But there are solutions for that.

There are however some problems left for that to really work. These mainly have to do with the speaker and listener positions and thus the coupling of the speakers to the room.

This is it. You have to think in poles and zeros.

A minimum phase filter has all it's zeros inside the unit circle, and so it's inverse is stable because all it's poles are inside the unit circle. But to fully cancel the original, you must have a perfect inverse. To reduce it, you must have something close to an inverse. I'm surprised that some off-the-shelf EQ tuned to a specific frequency could be close enough to being an inverse of a particular mode to result reduced ringing time. Saying that, Flloyd Toole has at least 40 years experience on me