AndreasN wrote on Sat, 25 September 2010 14:50 |
It's a common claim from the EQ camp that any phenomena that is indicated by a measurement system to be minimum phase is minimum phase. |
bruno putzeys wrote on Sat, 25 September 2010 10:17 |
When, in acoustics, someone says that a measured transfer function is minimum phase they most certainly mean it's a combination of a minimum phase transfer function PLUS a pure delay (which is NOT minimum phase). |
bruno putzeys wrote on Sat, 25 September 2010 17:17 |
There's no "EQ camp" claiming this. There is no such thing as a "minimum phase phenomenon". What exists is a minimum phase transfer function (=magnitude & phase response rolled into one). When, in acoustics, someone says that a measured transfer function is minimum phase they most certainly mean it's a combination of a minimum phase transfer function PLUS a pure delay (which is NOT minimum phase). |
bruno putzeys wrote on Mon, 27 September 2010 15:50 |
I think their understanding of minimum phase etc is good enough, but the link between "minimum phase regions" and sensibility of room EQ is assumed, not demonstrated. |
AndreasN wrote on Mon, 27 September 2010 10:31 |
There is actually a continual stream of practical tests that "proves" that the applied EQ/DSP treatment works as intended. |
Ethan Winer wrote on Mon, 27 September 2010 20:33 |
So what's the point? |
AndreasN wrote on Mon, 27 September 2010 06:35 | ||
Thanks for the clarifications! Sorry for the poor phrasing in the original post. What I was trying to address is the link between observation system and reality. Don't want to mention names here. There are however, in the room EQ industry, a typical assumption that parts of a room response is close enough to "being" minimum phase. Close enough that the resulting observed aberrations in frequency response can be corrected by minimum phase IIR filters where the poles and zeroes are set by virtue of the seemingly "minimum phase" behaviour in parts of the observed response. Typically done by finding areas where the excess phase calculation is flat. In other words, looking for "a pure delay + minimum phase" response in the room and then disregard the "pure delay" part. It doesn't seem to me that it's a procedure that have any physical basis. How is a delay+minimum phase response supposed to be corrected by a pure minimum phase response? (didn't intend to mention names, but here's an example to make it clearer) |
AndreasN wrote on Mon, 27 September 2010 12:35 |
Sorry for the poor phrasing in the original post. What I was trying to address is the link between observation system and reality. Don't want to mention names here. There are however, in the room EQ industry, a typical assumption that parts of a room response is close enough to "being" minimum phase. Close enough that the resulting observed aberrations in frequency response can be corrected by minimum phase IIR filters where the poles and zeroes are set by virtue of the seemingly "minimum phase" behaviour in parts of the observed response. Typically done by finding areas where the excess phase calculation is flat. In other words, looking for "a pure delay + minimum phase" response in the room and then disregard the "pure delay" part. It doesn't seem to me that it's a procedure that have any physical basis. How is a delay+minimum phase response supposed to be corrected by a pure minimum phase response? (didn't intend to mention names, but here's an example to make it clearer) |
AndreasN wrote on Mon, 27 September 2010 15:31 |
A typical "proof of virtue" is to show that standing waves are hitting the noise floor at some earlier time than previously measured. Exactly what one expects when putting less energy into the system at the resonant frequency! |
JohnM wrote on Sun, 03 October 2010 00:15 |
My position on the merits of EQ should be fairly clear from this article, which is also part of the help text you linked to: Why can't I fix all my acoustic problems with EQ?. |
JohnM wrote on Sun, 03 October 2010 00:33 |
The greater the cut, the greater the difference between the decay rates of the original resonance and the filter aimed at it. |
JohnM wrote on Sat, 02 October 2010 17:33 | ||
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Geoff Emerick de Fake wrote on Fri, 08 October 2010 15:01 |
I don't get it... |
jimmyjazz wrote on Sat, 09 October 2010 02:18 |
In the examples you show, is anything an actual measurement, or is it all theory? |
JohnM wrote on Fri, 08 October 2010 12:06 | ||
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I suspect you may be considering this in terms of providing a perfect inverse for a room's transfer function by means of suitably chosen biquads. Whilst the TF of a room response from a specific source position to a specific receiver position can be broken down into its constituent poles and zeroes, which can then be grouped as biquads, that of course does not make it invertible - there are non-minimum phase zeroes in most such responses, even at very low frequencies, hence stable inverses do not exist whether constructed from biquads or anything else. |
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My post was about EQ filters however, not biquads in general. EQ filters have constraints on their biquad coefficients to allow them to function as intended, they do not allow independent placement of the filter poles and zeroes. |
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I'll illustrate this with some Z-plane plots (I operate in a sampled data world ) and since the poles and zeroes come in conjugate pairs I'll only show the upper half plane - in fact, I've produced the plots to span a frequency range of 210Hz and will look at a 50Hz filter, so the area of interest is in the upper right quadrant. The first plot shows the pole and zero locations for a 50Hz EQ filter with a Q of 10 (using the RBJ definition of Q from filter bandwidth at half gain) and with gain of zero. The pole and zero are at the same location. The T60 annotation (433ms) expresses the radius at which the pole and zero are located in terms of the time the pole resonance would take to decay by 60dB, as a convenience for use when examining decays of acoustic resonances. |
Geoff Emerick de Fake wrote on Sat, 09 October 2010 23:32 |
Basically, what I don't get is you consider the influence of poles decay and apparently neglect that of zeros. |
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I don't understand what is an EQ filter with a gain of zero...An EQ filter has some boost or cut, so do you mean 0dB boost (or is it cut?)??? But a flat EQ has neither poles nor zeros...although I understand that, for the sake of demonstration, you may consider a flat EQ as identical denominator and numerator, which would obviously have their zeros and poles at the same location. Which is a perfect demonstration of the interaction between zeros and poles when they are very close. |
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I deliberately don't use Q notion because it just doesn't work for EQ's. IMO it works only for RLC bandpass filters. The academic definition of Q suppose asymptotic zero response and narrow BW. Eq filters never obey the 1st condition and 2nd condition is not applicable for less than 3dB boost/cut. |
Geoff Emerick de Fake wrote on Sun, 10 October 2010 14:45 |
Tell me if I understand you well. "common acoustical poles" seems to be a way of representing the invariant room accidents, in particular room modes, in a way that suit itself to equalization, which is the basis of this discussion. In this representation, room accidents are represented by biquads, with poles and zeroes. Now it seems that you don't do anything with this particular biquad zeroes because they are almost an act of God . But you take into account the poles of the EQ because they are perfectly and easily accountable. Honestly trying to understand; somewhat goes against 40 years of electronics engineering and a droplet of acoustics. |
bruno putzeys wrote on Sun, 10 October 2010 16:56 |
What algorithm do you use to get from a response measurement to a p/z representation? The reasoning that the poles remain in place while the zeros shift about is entirely correct as I see it. I seem to remember our company being contacted by a Finnish joint with similar ideas. |
JohnM wrote on Sun, 10 October 2010 16:24 |
I think something got lost in translation there, accidents? |
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Anyway, the transfer function from a source position to a receiver position in a room has a numerator and a denominator. The roots of the numerator are the zeroes of the TF, the roots of the denominator are the poles, which correspond to individual resonant frequencies in the TF. The closer the poles are to the unit circle in the Z plane or the imaginary axis in the S plane, the slower the associated resonance decays and the greater the peak in the frequency response due to that particular resonance - the overall response is the combined effect of all the poles and zeroes of course, but each has its contribution. |
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If we could move the room TF poles further away from the unit circle we would have a response that had smaller peaks and faster decay. We can't actually alter the poles of the room TF, but what we can do is put a biquad EQ filter in the path to the source for each resonance we want to target. The filter adds its own pair of poles and its own pair of zeroes to the TF. We can adjust the EQ filter cut and bandwidth so that its zero locations fall exactly on top of a particular pair of poles in the room TF. The net effect of a pole and a zero in the same location is nil, so doing this effectively eliminates the room TF pole pair we have targeted. |
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We are left with the pole pair of the filter itself, but the nature of EQ cut filters is that their poles are further from the unit circle than their zeroes, so overall the effect is as if we moved the room TF pole pair to the locations of the filter pole pair, where they have much smaller influence on the frequency response than they had in their original locations. |
Geoff Emerick de Fake wrote on Mon, 11 October 2010 11:35 |
That's where I lose you (or you lose me). What do you do with the zeroes of the biquad that is derived from the actual RTF? I understand when you say "I am not attempting to do anything about the zeroes of the room transfer function", I understand you can't change them, but my understanding is that the algorithm "translates" the actual RTF into a set of biquads with a set of poles and zeroes. My gut feeling is that the correcting EQ should have its zeroes and poles at the same location and they would both cancel. |
JohnM wrote on Mon, 11 October 2010 15:25 |
........ If the aim was to produce a perfect inverse of the room TF then you would indeed want to put zeroes on all the poles and poles on all the zeroes, literally invert the TF. That, however, is not possible. Room TF's have zeroes that are outside the Z plane unit circle/in the right half of the S plane. Poles in such locations would be unstable (their damping would be negative). So half of the answer is that this is not an attempt to make a perfect inverse because that cannot be done. ...... |
JohnM wrote on Mon, 11 October 2010 08:25 | ||
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Now we have something we can work with. Anywhere the excess group delay plot is flat is a minimum phase region of the response. |
AndreasN wrote on Tue, 12 October 2010 13:38 |
Real life is a signal leaving a speaker and bouncing around in a room. Modal response, standing waves, are waves passing the measurement mic at regular intervals. A reflective rectangular room will have clearly audible flutter echo from speaker to listener. That's the high frequency sound of a broadband lump of energy bouncing back and forth at regular intervals. Standing waves are typically filtered more towards the low end, but it's still "wave packets" of energy passing the sweet spot at regular intervals. That this repetition rate happens to be this or that Hertz is the product of the waves passing the microphones at those intervals. Not other way around! There's no "Hertz" in reality, only energy changes across time. |
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Minimum phase filtering will invariably give a very short time response compared to the acoustic response. |
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Having a single short impulse response altering the signal can not, even in the 2D world of digital signal processing, do anything to the long time behaviour. The rate of decay is still constant! The EQ can't do anything about the room and it can't change the rate of decay. |
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Looking at the calculated before/after filtering in the waterfall plots in REW confirms this. I've looked at the simulations for several different rooms and the results are the same. A -10dB EQ cut shows up as a -10dB cut across the whole decay range. It doesn't increase the rate of decay. |
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The modal EQ part in REW seems to calculate a shortening in decay rate that corresponds directly to the EQ cut in deciBels. |
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Cutting in the direct signal to counteract standing waves will leave a hole in the direct signal |
AndreasN wrote on Tue, 12 October 2010 15:11 | ||
PS, this part of your text is also a bit strange:
I've also looked at this aspect in several different room measurement. The only way I can find any part of the excess group delay to "be flat" is by not looking hard enough. As I zoom in, the response observed is never flat in any region of any room responses. |
AndreasN wrote on Tue, 12 October 2010 07:38 |
The situation is akin to strapping an EQ in front of a reverb unit. Twisting the EQ knobs can't change the amount of feedback circulation in the reverb patch following the EQ. Changing the sound of the 'verb unit needs to be done inside the 'verb system by altering the strenght of the feedback. Or, in real life, altering the strength of reflections in a room. |
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So I'm still utterly unable to see how minimum phase have any real world connection to room acoustics! |
AndreasN wrote on Mon, 27 September 2010 06:35 |
There are however, in the room EQ industry, a typical assumption that parts of a room response is close enough to "being" minimum phase. Close enough that the resulting observed aberrations in frequency response can be corrected by minimum phase IIR filters where the poles and zeroes are set by virtue of the seemingly "minimum phase" behaviour in parts of the observed response. Typically done by finding areas where the excess phase calculation is flat. In other words, looking for "a pure delay + minimum phase" response in the room and then disregard the "pure delay" part. It doesn't seem to me that it's a procedure that have any physical basis. How is a delay+minimum phase response supposed to be corrected by a pure minimum phase response? |
JohnM wrote on Tue, 12 October 2010 17:06 |
This is incorrect. To be pedantic, the time response of a typical IIR filter is, well, infinite but for a real world example simply make a measurement of a very narrow EQ boost and look at how long its response rings. |
Geoff Emerick de Fake wrote on Tue, 28 September 2010 14:32 |
Most of the "reverse impulse response techniques" end up doing just about the same as their purely EQ counterparts. Those techniques that are supposed to work at MF are plagued with a too-narrow sweet spot. |
JohnM wrote on Tue, 12 October 2010 17:06 | ||
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JohnM wrote on Tue, 12 October 2010 17:10 | ||||
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Geoff Emerick de Fake wrote on Wed, 13 October 2010 00:44 |
In your original post, you mentioned a membrane flapping: it is obvious that no EQ can correct this because it is both non-linear and time-variant, but reflections are enough linear and time-invariant, when they are significantly shorter than the period of the signal. Then, if the response has the shape and phase of a biquad, it is a biquad as far as processing is concerned. |
AndreasN wrote on Tue, 26 October 2010 13:44 | ||
Hmm.. Shorter than the period of the signal? Impulses doesn't have periods. |
AndreasN wrote on Tue, 26 October 2010 19:44 |
"Being sorta minimum phase" is obviously not the same as being minimum phase. At what point is the excess phase plot flat enough? 10 millisecond deviation? 1 millisec? 0.1 ms? It doesn't seem to hold up to scrutinous analysis. |
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Integrating 20ms (1/50Hz) is pretty common. Integrating several hundreds of milliseconds, as in a typical standing wave boom, seems a bit far fetched to me. |
AndreasN wrote on Tue, 26 October 2010 20:44 |
........ Another strange thing is that all the excess phase plots I've looked at, from real rooms, tends to be flatter in the high end than the low end. If one is to take this literally, EQ'ing high end should be better than EQ'ing low end.. We know it doesn't work that way. ........ |
Bogic Petrovic wrote on Wed, 27 October 2010 04:16 |
p.s. i can't do analysis without smoothing... REW ignore my attempts to switch off smoothnig... best i can get is 1/48 octave smoothing |
JohnM wrote on Wed, 27 October 2010 10:01 |
.........Boggy, in the REW Analysis Preferences uncheck the "Allow 96PPO Log spacing" box. That option allows REW to convert measurements to a 96PPO log spaced format if that reduces storage, but requires that the measurements be filtered to 48PPO. If you uncheck the box and just re-apply the IR windows you should get an unsmoothed response. |
AndreasN wrote on Tue, 26 October 2010 13:44 |
In any case, the situation is one where positive pressure is cancelled with negative pressure, and vice versa. |
AndreasN wrote | ||||||
This situation is different. If looking at a pure minimum phase response, the excess phase plot is absolutely flat no matter how far one zooms in. "Being sorta minimum phase" is obviously not the same as being minimum phase. At what point is the excess phase plot flat enough? 10 millisecond deviation? 1 millisec? 0.1 ms? It doesn't seem to hold up to scrutinous analysis. |