Linkwitz transform

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The response of the LT filter looks a lot like a kind of special shelf filter. It has a response shape (including phase response) that is designed and intended to work with drivers in a closed box, whereas a shelf filter is more generic and will not necessarily do what the LT can do.

Since the LT is based on a driver's TS parameters and these change as the cone excursion increases (yes, in real time while the cone is moving!) the LT will also not be a perfect match to the driver's instantaneous response (e.g. frequency response). As a result, if you can get "close enough" with a shelf filter the result will probably be just as good as with an LT.

Note that "EQ" like a single parametric EQ band (PEQ) is NOT at all like the LT filter. It's theoretically possible to use several PEQ bands to better approximate the LT, but together they will still not be like a shelf filter. Again, close enough might be good enough. It depends on exactly what you need the filter(s) to do, and whether they are capable of adequately doing that.
 
Thanks. I have designed a sealed enclosure that gives me a Qtc of 0.707, and I am quite happy with the size, e.g. I don’t need to make it smaller for aesthetic or practical purposes. A linkwitz transform (hardware or DSP based) will not give me any further benefits (lower extension) in this case, correct?
 
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Thanks. I have designed a sealed enclosure that gives me a Qtc of 0.707, and I am quite happy with the size, e.g. I don’t need to make it smaller for aesthetic or practical purposes. A linkwitz transform (hardware or DSP based) will not give me any further benefits (lower extension) in this case, correct?

Yes, it will allow to extend your response lower......if you want to.

But, since you've selected a driver and selected a box, you've already "locked in" many of the system parameters. (Power requirements, SPL capability, etc.)
A Linkwitz Transform EQ can only extend (within reason) the response of a system.
There's no free lunch on any of this stuff. :)

Dave.
 
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That is soooooo mathematically elegant.

But wouldn't it make much much more sense to just put a mic where your head normally resides when listening to music and tweak accordingly?

Absolutely not. If using an iterative approach to optimize a subwoofer LT function, I would put the microphone 1" from the woofer center cap.

Room EQ is another can of worms totally. :)

Dave.
 
Using two state variable circuits, the scheme presented by french youtuber Jipihorn shows that the mathematical operation of the Linkwitz transform consists of a circuit having an inverted transfer function of the transfer function of the loudspeaker (fo, Qo) followed by the desired transfer function (fp, Qp).

Roughly written :
Linkwitz's transform transfer function = (fo, Qo) * 1/(fo, Qo) * (fp, Qp)

The circuit :

https://jipihorn.files.wordpress.com/2013/06/linkwitz-variable-state.pdf

The link (video in french) :

Linkwitz et filtre a variable d’etat : mise en oeuvre | Jipihorn's Blog

The processor way

Using BSS, Behringer, Yamaha or similar processors, it is possible to obtain the same results using three main equalisations.
ARTA is of great help to see how it is simple to overlay an equalised frequency response with a target frequency. The results can be very accurate.

1. use the bell equalisation at the resonance frequency to transform
fo, Qo --> fo, Q=0.707

If Qo > 0.707, set the Q value of the parametric equalisation to Qo, the level being set in negative dB,
for example Qo = 1.0, set Q = 1.0 and level = -3.0 dB

If Qo < 0.707, set the Q value of the parametric equalisation to 0.707, the level being positive dB
for example Qo = 0.57, set Q = 0.707 and level = +1.8 dB

I may say that I've still have to see this method of Q manipulations applied by somebody else..

2. use the 12 dB shelf equalisation to get the desired target resonance frequency
fo, Q=0.707 --> fp, Q=0.707

3. using another bell equalisation to get the target damping coefficient Qp
fp, Q=0.707 --> fp, Qp

The shelf equalisation in processors is often limited to +/- 15 dB. However using two or three shelf equalisations is possible, the settings have to be controlled by the frequency responses shown by ARTA.

Possibly some minor equalisations adjustements may be needed to get a target frequency response with a precision of 0.2 dB or better.

Be aware that the Q value is not defined in the same manner in all processors. The above quoted processors are in agreement with those defined by Rane and used in standard loudspeakers practices.

I applied such digital transforms for woofers, mediums and tweeters on a BSS since ten years.
 
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Room EQ is another can of worms totally. :)
Are you calling my music room a can of worms?

Mock horror aside, let's talk real-world life.

After you've made your one-inch mic test look great (esp if you have the sense to go for a proper house-curve instead of arbitrary nice-looking curve), you then start to scrap (often quite substantially) the careful filters you just carefully calculated in order to correctly tweak it for your room. It doesn't matter in any way what so ever what prior Linkwitz EQ you may have dialled-in. The Linkwitz EQ will be undetectable when you look at your final EQ.

Yes, I'd say the same thing about sticking a low resonance woofer into a tiny box in the vain hope of landing on a good-looking one-inch curve with a Q of .7. Destructive use of a good woofer.

So why bother getting the one-inch performance right?

We all love the fun of R&D. The Linkwitz approach is a fun thing to explore for a serious enthusiast. But I'd like to hear anybody who has done any room EQ deny the practical good sense* of my "scrap" paragraph.

B.
*I'm just finishing the great Ben Franklin biography by Isaacson; highly recommended
 
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The Linkwitz EQ will be undetectable when you look at your final EQ.


So why bother getting the one-inch performance right?

I think there are four tuning stages to getting desired performance,
and they should be accomplished in order IMO

Speaker tuning that is room independent.
Room/listening spot tuning, based on speaker placement and room acoustics.
House curve for tonal preference.
EQ necessary for source material variations.


It's best if room independent speaker tuning is handled with its own processor, and not touched once right. The Linkwitz transform fits here.

EQ necessary for source material, is also best handled on it's own, given the great variability in material.


Which kinda begs for Room Tuning and House curves to also have their own domain....

But since it's a little unrealistic to expect folks to have separate EQ/processing stages for all these, we have to choose where to combine them........

I'd say two stages minimum though.


Trying to put all four into one stage/processor is endless fiddling and futility IMHO.
Putting all four together also keeps us from understanding what we are actually trying to correct.
 
I presume stage number is of no consequence when processing digitally?

Interesting question...because it invokes the logic behind "why stages"?

Source material, is an input, so EQ should be applied at the onset to fix it, before all the downstream consequences. It's the first stage in physical processing chain. This EQ could be done speaker independent!

Speaker tuning, output that is room independent, with all its xovers, mag/phase/time alignment,.... is the last stage in the physical processing chain. It could be done source independent !

Room tuning/house curves... are in between the input and output adjustments. They are done totally room/placement/preference dependent !

It's the logic and sequence that matter...
Whether it's digital or analog, doesn't matter.
 
It's the logic and sequence that matter...

Mark100 has said many smart things, no question.

But there's no logic or sequence. That's just his sense of Cosmic Orderliness and basically just an aesthetic choice. Mark100's reply to scottjoplin's subtle question was well-meant and carefully presented.

But there's nothing convincing in the reply: the stages simply do not build on one another. They replace one another. Might as well make a good speaker in an ample sealed box with the lowest Q possible* and EQ in-situ.

B.
*we're talking about reproducing music using a characterless speaker, not making music with an instrument
 
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I have hesitated to poke into this discussion, but feel the urge.. .

I have equalized speakers at 1" and listened. Then I have equalized for the room, and listened again. In every case, I have preferred the speaker eq over the room eq, by a pretty large amount. My comparison was done against live music in one case, and the room eq was much further from "live" than the speaker eq.
 
Mark100 has said many smart things, no question.

But there's no logic or sequence. That's just his sense of Cosmic Orderliness and basically just an aesthetic choice. Mark100's reply to scottjoplin's subtle question was well-meant and carefully presented.

But there's nothing convincing in the reply: the stages simply do not build on one another. They replace one another. Might as well make a good speaker in an ample sealed box with the lowest Q possible* and EQ in-situ.

B.
*we're talking about reproducing music using a characterless speaker, not making music with an instrument

Ben, I would suggest you study large scale, live touring sound. These guys don't care what system they use, they don't care about what they themselves think they can hear.
They care about providing pleasing sound. The principles they employ reflect that goal.

The stages / logic that i outlined are simply what I've learned about logical, step by step, set-up and tuning to provide excellent audio....wherever, be it mega festival...or even in a room :)

You're right the stages do not build on each other, ....blessedly ! No more building crooked on top of crooked, ....all trying to balance the crooked that's below them!!!!
They can't replace each other,.....that's the last thing they are meant to do..
They can't... that's the whole point ;)
 
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I have equalized speakers at 1" and listened. Then I have equalized for the room, and listened again. In every case, I have preferred the speaker eq over the room eq, by a pretty large amount. My comparison was done against live music in one case, and the room eq was much further from "live" than the speaker eq.
Obviously it's impossible to know what went wrong there without seeing your measurements and EQ. I would suggest a couple a possibilities. Firstly that your setup is very sensitive to listening position, and secondly the combined EQ was too much, it's often better to EQ too little than to EQ flat depending on how much is required for a flat response.
 
In every case, I have preferred the speaker eq over the room eq, by a pretty large amount.

Just wanted to add a word in addition to scottjoplin's good post.

If your one-inch result sounds better than your listening-chair result, then I am puzzled about how that can come about. And here I re-introduce a concept only slightly raised so far: house curve.

How can you have a better result than the one that works at your chair. I can't imagine what you are aiming for at your chair if - when you are all done - you say, "Gosh, that stinks".

There is no objectively correct curve, no matter what we all heard in high school physics, absolutely perfect speakers playing in anechoic chambers possibly excepted. The correct curve is the house-curve that you like delivered to your chair.

B.
 
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