john k... said:
That's not quite true and it's not because of some trivial detail- it misses the whole idea of why minimum phase is defined the way it is.
Consider the set of all linear, time-invariant, causal, and stable systems. The minimum phase systems are the invertible members of this set. To be clear, "invertible" means has an inverse in this set.
In terms of the properties of the system, a LTI system is minimum phase if and only if it is causal and stable and has a causal and stable inverse.
The point is that what a minimum phase system does to the signal is reversible by a realizable (LTI, causal, stable) filter.
Here are a couple counterexample to your assertion:
- an allpass filter is causal and stable but does not have a causal inverse
- a highpass filter is causal and stable but does not have a stable inverse (pole at 0)
markus76 said:
Markus
It turns out the the lowest mode of any room is independent of shape and depends only on the floor plan (or largest surface actually if the room is very tall). Thus calculate the lowest mode for a rectangle of the same floor space and you know what the frequency will be for any shape. The mode shape differs of course, but not the frequency. An interest result from my thesis, but it can also be proven in other ways, like the Rayleigh Coefficient.
Rybaudio said:
Yes, I should have mentioned that. I was trying to express it without saying poles and zeros and mess up. It happens. Causal and stable require poles in the left half of the s plane. Having a stable inverse requires the zeros also be in the left half plane. Stable, causal with stable, causal inverse is MP. So I would just add that MP implies not just invertible, but a stable, causal inverse.
Thanks for picking up my error.
inertial said:Thanks Dr Kreskovsky,
My math is worst of my english!
So a LTI system can be MP or not. But if a system is MP , is it automatically LTI ?
MP is usually discussed in the context of LTI system.
Yes.
We should be able to consider it LTI.
When we apply digital room correction ( for one point) are we correcting only the amplitude or also the time?
Perdone my confused exposition
Paolo [/B]
Only amplitude is for sure, assuming the correction is MP. But it doesn't have to be MP eq.
This is important IMO, I have to reflect why you do not have answered " absolutely yes" ........john k... said:
john k... said:
Ok, if we use FIR filters we can correct both amplitude and time ( in one point ), is it this how" Digital Room Correction" works? And can we assume the procedure is mathematically rigorous-correct?
Many thanks,
Paolo
inertial said:
Because I'm not a structural engineer and I can not assume that the room structure and other damping behaves linearly. Most likely for audio the assumtion of the room being LTI is a good one.
In theory FIR filters can unwrap the phase. But this results in a non causal filter, and I don't know off hand if these will always be stable. Lack of causality can be corrected by introducing a sufficient delay to shift the impulse to the right on the time axis and then truncating the remaing negative time part of the impulse. I can not speak for the various room corections algorithms. Many are based on MP eq. Those can be based on IIR or FIR approaches. If they correct phase then I would assume they are predominatly FIR.
gedlee said:
Could it be that this was actually the result of an adjacent chamber such as a crawlspace?
Most homes where I live have framed drywall structures over solid concrete foundations. Those aren't too bad because the walls and ceiling are lossy enough to provide some damping. There are a few though that have hardwood floors over a crawlspace, and in those, the crawlspace forms an acoustic chamber. So there are actually two resonant spaces that are tightly coupled, one the room and the other, the crawlspace.
Those are tough to deal with. There are things you can do to modify the resonance and damp the adjacent space, but I've never really been satisfied with any listening room that has a hardwood floor over a crawlspace.
john k... said:
John
I think that it is safe to assume that the room structure is linear and time invariant. This of course is not so true of the loudspeakers, which are in most cases are neither linear nor time invariant. To what extent this is true is going to be highly dependent on the loudspeaker. I think that the time invariance may be the bigger complication than linear in room EQ systems. At what sound level and driver temperature is the EQ done? If the system has considerable thermal variances then the complications could be quite serious. This is why I attempt to do systems with high thermal stability and crossover designs that are as insensitive to the driver impedances as possible. An electronic EQ that assumes LTI for a system which is not could be a serious problem. The pro guys know this and develop very complex means of tracking thermal changes in the EQ. In Hi-Fi this factor seems to be ignored for the most part. In a small speaker the thermal effects can be quit substantial.
gedlee said:
Maybe you have a different sort of construction than what I'm referring to. What I'm talking about are homes that have a crawlspace underneath for access to pipes and what not. The room and the crawlspace are tightly coupled because they share a boundary that is free to vibrate - the floor.
In the homes I've been in that had crawlspaces, the acoustics was terrible as a direct result of the crawlspace. The chamber under the floor is the worst case I can think of because the ground is obviously rigid and the four side walls are too, usually brick or rock in compression from the weight of the home. No damping materials inside the crawlspace. Modal resonance inside the crawlspace is huge, worse than a basement or bathroom. And the listening room shares one surface with it - the floor. The floor acts like a vibrating "membrane" with the crawlspace chamber underneath it. Both chambers are coupled by the floor because they share it.
A crawl space like you suggest will in general cause a loss of energy in the room not a peak. Its basically a tuned absober where the floor is the membrane. The coupling between the space below the floor and the main room is not what I would call high. For the coupling to be "high" the floor would have to be very flimsy - it would have to flex with just walking on it. This doen't seem typical to me, but crawl spaces are not at all common here.
"....
I think that it is safe to assume that the room structure is linear and time invariant.
...."
Although the effect might be small, I have wondered about the time invariance.
This is my thinking: A speaker on one wall, the opposing wall 20 ft (about 20 msec) away and a microphone in the middle (10 msec away). Let's ignore other boundaries to keep it simple. I will also ignore issues of measuring frequency resolution when analyzing with short time windows.
At the microphone, for about 20 msec, you will be measuring the Freq Response of the speaker. However after 20 msec the rear reflection will now interfere with the ongoing output of the speaker. You now have a delay-and-add filter (comb filter) on top of the speaker's response.
So would the speaker and the room as a system still be considered time invariant? Yes, I have not forgotten that I am conveniently ignoring that the speaker by itself is not time invariant.
I think that it is safe to assume that the room structure is linear and time invariant.
...."
Although the effect might be small, I have wondered about the time invariance.
This is my thinking: A speaker on one wall, the opposing wall 20 ft (about 20 msec) away and a microphone in the middle (10 msec away). Let's ignore other boundaries to keep it simple. I will also ignore issues of measuring frequency resolution when analyzing with short time windows.
At the microphone, for about 20 msec, you will be measuring the Freq Response of the speaker. However after 20 msec the rear reflection will now interfere with the ongoing output of the speaker. You now have a delay-and-add filter (comb filter) on top of the speaker's response.
So would the speaker and the room as a system still be considered time invariant? Yes, I have not forgotten that I am conveniently ignoring that the speaker by itself is not time invariant.