Acoustics of corners

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Consider the standard physics representation of a signal as a complex exponential V(w) = A(w) * exp^(i * w * t) where w is angular frequency and t is time. This describes a vector that rotates around the origin with an amplitude of A and it makes w full rotations every second. At any instance in time there is a "phase" of this vector, but as time progresses this phase continuously advances. This means that phase and time are simply two different ways of describing the exact same thing - progression of time or progression of phase. They are the same thing not different things.

This is easier to see in the analog domain as things get a little foggier in the digital domain.

Thanks, I'm ok with the math, I get that one equates to the other.

It's the words and how we use them that i've been trying to provide focus on.
"Time delay" is a commonly used term, most often as a constant delay IMO...I just can't see that it fits into the math as just presented.

I've struggled a long time to get what I believe is a pretty good handle on phase...a lot of that struggle has been trying to understand what folks mean with their definitions, when half the time I think they don't understand either! lol
 
Most often we think of "delay" as being far greater than a simple delay that rotates the phase by < 2 PI. "phase" is an instantaneous value for a signal, but when we talk about a transfer function then we have a fixed phase at any given frequency. So "phase" could be thought of as having a different meaning in the time domain that it does in the frequency domain.

A fixed time delay will yield a constant slope of phase with frequency in a transfer function. Most real measurements have a variable phase and we can calculate the "group delay" which is the delay at any given frequency, by looking at the slope of the phase curve at that frequency.

Because these are all complex analytic functions they are forced to obey the Cauchy-Rieman conditions which ties the magnitude response to the phase response for "minimum phase" systems.
 
To get perfect phase alignment (time alignment) i use this all pass filter for the dipole subwoofer, Project 103 - Subwoofer Phase Controller
This analog filter is not ideal since it continue to delay below the crossover point. And then add the LR 24dB filter at 200Hz and another 24dB filter at 27Hz. and as i mentioned the infra low sub that is place in the "wrong" end of the room (built in the wall).
Thanks Earl for your energy and your constructiveness and no nonsens !!!! Love ya!
I understand that you preffer to do things "right" in the first place and do digital correction if neccessary later. I agree. What do you say about a program as rePhase? Whats the drawback?
 
What do you say about a program as rePhase? Whats the drawback?

The drawback with automated techniques like this is that while they can certainly do wonders with a poor situation, many think that the same can happen with a good one. Studies have shown that automated EQ can often degrade a situation and as such are not a panacea.

When I started my quest things like "rephase" did not exist, even DSP was in the distant future, and yet I was able to achieve results that equal what is being done with these newer technologies. I find no need to implement them now as they just tend to add cost and complexity without any significant improvement.
 
When I started my quest things like "rephase" did not exist, even DSP was in the distant future, and yet I was able to achieve results that equal what is being done with these newer technologies. I find no need to implement them now as they just tend to add cost and complexity without any significant improvement.

Here's some of the easy to see things dsp and FIR can do that offer significant improvement..and I would hazard to say, could probably make at least some improvement to any design ever made ...:)

I'll ignore things any active DSP can do such as precise time delay and precise level matching, and comment on improvements only FIR can provide.


Practically unlimited minimum phase EQs can be embedded into FIR files to correct individual drivers response variations, which are minimum phase.

The ability to flatten phase of individual drivers without altering any magnitude response previously corrected.

The ability to use linear phase x-overs that do not induce group delay.

These are simply real improvements IMO, that no amount of passive work can hope to fully replicate.
 
Here's some of the easy to see things dsp and FIR can do that offer significant improvement..and I would hazard to say, could probably make at least some improvement to any design ever made ...:)

I'll ignore things any active DSP can do such as precise time delay and precise level matching, and comment on improvements only FIR can provide.


Practically unlimited minimum phase EQs can be embedded into FIR files to correct individual drivers response variations, which are minimum phase.

The ability to flatten phase of individual drivers without altering any magnitude response previously corrected.

The ability to use linear phase x-overs that do not induce group delay.

These are simply real improvements IMO, that no amount of passive work can hope to fully replicate.

I think that I have a pretty good understanding of what DSP can do in loudspeaker design.

I have made all my speakers in both active and passive versions and I have found that the differences are negligible not a "significant improvement" as you claim.

My current speakers are active and the complexity is simply not worth it, so I am going to redo them passively. That's how much I believe in DSPs "significant improvements". I do use DSP for my multiple subs.
 
I think that I have a pretty good understanding of what DSP can do in loudspeaker design.

I have made all my speakers in both active and passive versions and I have found that the differences are negligible not a "significant improvement" as you claim.

My current speakers are active and the complexity is simply not worth it, so I am going to redo them passively. That's how much I believe in DSPs "significant improvements". I do use DSP for my multiple subs.

Sorry if you felt I was inferring a lack of understanding re DSP, I meant to be addressing the forum at least as much as posting to you. Besides, I'm pretty certain you've forgot more about signal processing than I've learned yet :)

It's great you have the ability to replicate active with passive.

In your active setup, did you try any linear phase x-overs, or phase flattening of drivers before summation?
This is where I think I keep hearing real improvements...

If you've played with FIR, I'd be interested in how and your thoughts about it, ....as I'm an obvious, perhaps over-zealous, advocate of it..
 
You talk about the signal to the drivers. You don't say much about your acoustic situation. How much can DSP help there? It seems that the program you mention is seen as something to be used on the whole.

Hi, still not sure what you're asking.
Isn't the acoustic situation just the sum of the drivers put together?

The program, rePhase, can be used on whatever you choose, individual drivers, or the summed system response.
I mean it's just a batch of filters in the end...what do you want them to do? Work on the parts or on the whole? Or both if you want
 
In your active setup, did you try any linear phase x-overs, or phase flattening of drivers before summation?
This is where I think I keep hearing real improvements...

If you've played with FIR, I'd be interested in how and your thoughts about it, ....as I'm an obvious, perhaps over-zealous, advocate of it..

If phase aberrations are audible continues to be a debated point. No blind tests that I know of has shown it to be significant.

In my speakers the woofer sets several inches ahead of the tweeter, so they are time aligned after the crossover. I checked this and found that over the whole band the total phase variation was < 60 degrees, and through the decades around the crossover it was < 30 degrees, so basically, the phase of the system already is linear.

From what I can glean about phase audibility is that is a small effect unless it is very far out of whack, then something like Rephase might have a notable effect.
 
Regarding corners: This paper shows the complexity, but also that corner absorbers, here active, can work
https://infoscience.epfl.ch/record/...stic absorbers in the low frequency range.pdf

You can't compare an active absorber with a passive one. All I have seen data for in this thread is a passive one, which has not shown much effect at all. Active would be very effective, but a completely different animal.
https://infoscience.epfl.ch/record/...stic absorbers in the low frequency range.pdf
is passive AS in needs no power source. And active AS in generates current and voltage:)
I retracted the active statement in later post.
By the way the authors has now presented an true active version that works over a wider freq. range.
Still an absorber for corners. So back to original question. Absorbers in corners can work.
 
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