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Minimum phase and acoustics

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AndreasN:
Hello!

Have a question regarding minimum phase in acoustics. 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.

Disregarding measurement systems for a while - is there a physical rationale behind such an assumption?

If a current in a voice coil makes a magnet move, that's a direct cause and consequence. That's minimum phase. So far, so good. If the membrane attached to the magnet starts flapping, it's not a direct cause->consequence, it's an indirect consequence. Ditto with edge diffraction and... Anything involving interactions between direct sound and reflections from a room! As in acoustics in general.

So how come some claim certain acoustical phenomena are minimum phase and hence can be corrected by EQ? I can't wrap my mind around this.. It seems to me that it's an outlandish claim. But I'm apt at jumping at too quick conclusion.

Thoughts?


Regards,

Andreas Nordenstam

bruno putzeys:
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.

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).

You can get an idea of whether a measured impulse response is that of a minimum phase transfer by looking at how it decays. If you see no echos or ringing bigger than the initial spike you can be reasonably sure that it's MP.

There's something pretty crucial about this. The response of a driver mounted in a cabinet, measured more or less on axis in a more or less reflection-free environment, is usually minimum phase (+delay). Turn the cabinet around and it's no longer the case. The first thing to hit the mic is the diffraction (a weak spike) followed by the first reflection which is much louder.

That's why you can't say some physical process is minimum phase. The response from the same speaker, as measured in different environments or from a different angle may or may not be minimum phase.

Minimum phase has several implications:
1) phase response can be derived directly from magnitude response and vice versa.
2) The phase responses of two MP transfer functions that have mirror-image magnitude responses (in dB), are mirror images as well.

Analogue EQ's normally have MP. If you use one to correct the magnitude response of another MP transfer function, the phase response is corrected as well. By necessity this means that the impulse response is also corrected. For instance, when designing a loudspeaker you're best off first correcting each drive unit separately, precisely because of this. A single wideband loudspeaker unit with an EQ in front of it can have a spectacularly tight impulse response, even if the same unit without EQ does not.

Non-minimum phase transfer functions can be corrected as well, to an arbitrary degree of precision but never exactly, and always at the expense of added delay. The complement of a non-minimum phase filter is a non-causal filter (one that has "pre-decay"), which can be approximated using an FIR filter provided you add as much delay as the amount of "pre-decay" you actually want to realise.

Thomas Jouanjean:
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).





And a pure delay in acoustics is very hard to achieve in a studio situation, for example because of the material's density vs behaviour with regards to different frequencies.

AndreasN:
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).


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)

bruno putzeys:
Oh well I think the opinion held "here" with regards to room EQ in general is sufficiently known

As your link shows, people run a lot of numbers on these problems whilst utterly failing to grasp the fundamental issues. Running through the text (approx. 20 seconds) 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.

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