JohnM wrote on Fri, 08 October 2010 12:06 
Geoff Emerick de Fake wrote on Fri, 08 October 2010 15:01  I don't get it...
 I'm not too clear from your post what you don't get exactly, but I'll expand on my comments, which may help either make clear what I'm saying or provide some specifics for objection.

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 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 nonminimum phase zeroes in most such responses, even at very low frequencies, hence stable inverses do not exist whether constructed from biquads or anything else.

As I mentioned earlier, this discussion would not even have started if we didn't agree on the fact that there is a domain where the approximation is valid, and all arguments/discussions/fights are based on that assumption.
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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.

I agree, that's why I've expressed the transfer function in s notation earlier.
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I'll illustrate this with some Zplane 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.

That's where you're starting to lose me. Having left school 40 years ago doesn't help either.
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.
Your example showing the dramatic reduction of decay at 50Hz goes to show that there is something that reduces the overall decay of the room + EQ combo. If you took into account only the poles, you would add both decays.
In fact it is a superb demonstration that EQ can compensate some of the timerelated effects of resonance, just like a 10dB cut can perfectly compensate a 10dB boost at same frequency and same BW. The way the decay at 50Hz aligns almost perfectly with the 6090Hz range decay says for me Mission accomplished.
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. [/aside]