Understanding Grimm Audio XO

[gainphile]

I find their approach is very interesting.

http://www.grimmaudio.com/whitepapers/speakers.pdf

1. EQ the drivers beyond operating range to flat

2. Apply the intended crossover, eg. LR4.

3. Apply time delay.

So far so good. But what about this 4th step, quote ..

Finally, the icing on the cake. The sum of an ideal LR4
system is a second order all-pass with a Q of 0.7. In order
to avoid the problems associated with correcting
phase exactly, build an inverse all-pass filter based on
the theoretical ideal. This filter will be non-causal so
there’s a good reason for using FIR.


Questions:

- What do they mean by " The sum of an ideal LR4
system is a second order all-pass with a Q of 0.7" ?

- What do you think " an inverse all-pass filter based on
the theoretical ideal" ?

If this can be realised using MiniDSP it would be great I think.

[GDO]

In my understanding:
you
1º LR24 filters are non phase linear filters which happen to have same (or similar) group delay pattern as a 2º order all pass filter.

2º Consequently, if you reverse this all pass filter, the product ( convolution) of the new filter (reversed all pass) and the LR24 will give you a "linear phse" LR24.

Hypex promised to make this feature available in their DSp products some time ago, but it seems that Grimm is their only user... But you can do this thanks to other providers.

You can generate a FIR filter like this (reversed allpass) with a soft as Acourate and use Convolver to eq your LR24 into a linear phase filter.

Or you can use Thuneau Arbitrator which doeas somerhing similar the IIR way.

[aczern]

from interview with Siegfried Linkwitz
Audioxpress 7/2011

"JD: Looking at your Orions, I can’t
but wonder whether that purposedesigned
analog crossover cannot be
replaced by a DSP unit?
SL: In principle, I am convinced that
it can be done. But it’s not trivial. You
need to measure and adjust the whole
chain, analog in to sound out. Now
someone may come up with an FIR filter
that makes everything linear phase,
but you get pre-ringing from the filter
and the sound may combine correctly
at one point in space but what about
off-axis?
You could use IIR filters to mimic the
analog filters, and that would probably
be my approach. Then I would first
make the amplitude response correct
and then you can do an overall phase
response correction of the complete
system. That’s how Bruno Putzeys
does it in his Grimm Audio two-way.
And I would not buy a standard DSP
box off the market. The devil is in the
details. But it’s hard, and it’s not on my
to-do list!"

[stoc005]

Go to Active Filters
What is called allpass or reversed allpass is also called delay correction by S. Linkwitz. See his analog implementations. It "fixes" the phase error of the 4th order LR filter and provides the phase correction needed. Used with success in the Orion active XO. To me a changing of phase is all about delay.

[Joachim Gerhard]

That is not a problem. 4th order Linkwitz wit IIR and phase correction with FIR. No pre ringing. Higher order then 4th bring that problem. Done that, been there. In 1993 in Essex. I talked to Bruno that we where first. Maybe he found the solution all by him self but i do not trust that.

[Davey]

Originally Posted by gainphile

I find their approach is very interesting.

http://www.grimmaudio.com/whitepapers/speakers.pdf

1. EQ the drivers beyond operating range to flat

2. Apply the intended crossover, eg. LR4.

3. Apply time delay.

So far so good. But what about this 4th step, quote ..

Finally, the icing on the cake. The sum of an ideal LR4
system is a second order all-pass with a Q of 0.7. In order
to avoid the problems associated with correcting
phase exactly, build an inverse all-pass filter based on
the theoretical ideal. This filter will be non-causal so
there’s a good reason for using FIR.


Questions:

- What do they mean by " The sum of an ideal LR4
system is a second order all-pass with a Q of 0.7" ?

- What do you think " an inverse all-pass filter based on
the theoretical ideal" ?

If this can be realised using MiniDSP it would be great I think.

Take an analog textbook LR4 crossover and sum the two outputs together and look at the transfer function relative to the input and you'll see the second-order all-pass function.

An inverse all-pass filter would yield an opposite phase response to what you just observed. Then, if you apply it to your textbook LR4 crossover the final phase response would be linear.

Regarding the a MiniDSP solution......I'm afraid not. The minidsp can add pure delay or create an all-pass function, but it can't create an inverse all-pass function. You need something more advanced to create that correction. A FIR based system or some sort of reverse-processed IIR filtering like used in the Thuneau.

Cheers,

Dave.

[GDO]

Pre...what?

[gainphile]

Thanks all, that clears up a lot of things! So in summary
- It is a good (smart) idea, even supported by SL
- It is a phase correction of IIR filter, using FIR
- It has the benefit of IIR filter and FIR, without the drawbacks of FIR.
- It cannot be implemented with MiniDSP (IIR).

So there is no way of creating the inverted allpas using Biquad for example?

[Joachim Gerhard]

Yes, the mixture of IIR and FIR cuts the mustard.

[phase_accurate]

At least with ADI's Sigma DSPs one can build subtractive-delay crossovers. These have properties that come quite close to the properties of the phase-correction plus LR approach.

Maybe they could also be done on a Mini DSP.

Regards

Charles