Zero Delay SVF and Allpass based filter.

[Tepeix]

A sort of experiment allpass based filter close to a Zero Delay Feedback SVF filter.
For curiosity.. But maybe as degraded but little optimized version ?? (the coefficient of the allpass could be approximated more easily i suppose)

Seams close but the difference occurs when using resonance..
The resonance is not zero delay... While the allpass seams without to strangely behave like zero delay ????
And how could we try to make it zero delay if possible ?)

Then testing it for variable cutoff, it seams to remain stable.. But maybe i need more stress test or analyse ?..

héhé that's really a strange discovery for me

[Tepeix]

Reading more the famous book : https://www.native-instruments.com/file ... _2.1.0.pdf

There's a mention to allpass substitution at page 92.
(yet i'm not sure to really understand what is said about)

[Tepeix]

This structure, with a 2th allpass. Mimic in a other way a SVF Zero Delay Filter.

Yet i'm very happy to find this strange thing, but there's a lost parameter in the equation... ...

Subtracting the allpass from the original we get the BP.
Then we take the second "pole" of the allpass, multiply by this parameter, and subtract to separate LP and HP...

It's possible to get the same response as a SVF for 0 to 1/4 nyquiest..

But how to calculate the value of this new coefficient ???

[Tepeix]

I think i find an approximation... Don't ask me how..
Was laughing to see it working because how much i try blindly to map some tan value to fit...

So in this particular allpass the value of coefficient are from 0 to 2.
For no res, the multiply value to get the LP normalized are C1 + 2-C2. (at least for 0 to 1/4 nyquiest)

To add res, we divide the frequency at the input of the C1 coefficient.

I this case i find that we have to do C1 +(2-C2) + C1*(a function close than tan)

So finally we have this : as Q is from 1 to 0 for more res: ((tan(1-Q)*(pi-((1-Q)*pi/2)))*((pi/4+(1-Q)) *C1) +C1+(2-C2)

... Now i don't even know if this really mimic a Zero Delay SVF...
Problem is that it doesn't work after 1/4 nyquiest... But maybe some more modification might be made..

[Tepeix]

Going back to the first way.. With 1th allpass..
(seams like 2th allpass have some unnatural response when trying to mimic analog circuit...
unless maybe just adding resonance ??)

Finding an optimization to only use 2 allpass instead of 3. Then the miracle happen !!)

It seams possible to really mimic the resonance of a Zero Delay Feedback SVF with allpass !!

The problem is that i have now 3 more parameter that need to be adjusted ;( ;(

Finally using the bp and not lp as the main feedback, it's possible to adjust adding also the hp and compensate,
which strangely seams to perfectly mimic the zero delay !
A paradox because there's obviously a delay ! Does this go in the future ??

But now the volume of the bp and hp might be compensated..
Also the level of hp re-injection might be calculated... Don't know how yet...

[martinvicanek]

Perhaps there is a misunderstanding about zero delay feedback filters. They do have delay in the transmission, as any causal filter must have. In fact the SVF has exactly the same transfer function as a direct form biquad. The term „zero delay feedback“ comes from a particular topology (delay-less loop) which is dismissed in textbooks as allegedly unsolvable. The argument goes like this: you cannot solve an equation like x = 2*x -1, because in order to compute x on the left hand side, you have to plug in x on the right hand side, which is unknown. But of course we can solve that equation quite easily to get x= 1.
The zero delay feedback topology has some advantages over direct forms, i.e. it handles low frequencies much better, and it is stable against fast modulation.

[Tepeix]

Yes, in fact not going to the future, there's always a state which i do not see as a delay..
But maybe we could say that it's a sort of delay, while the coefficient and/or structure make it like there's not.. ??)

But i was surprise as here, it look more like a sort of simple feedback, But mixing BP and HP there's a way to compensate and give the same response as a zero delay topology with allpass substitution..

But i don't know if there's any advantage to make this "allpass substitution"...
As now there's the need to find 3 or 4 more coefficients..
At some frequency cutoff the BP and HP feedback might be mixed differently.. So 2 Q value..
Then the BP and HP need to be normalized..

But it's some attempt to see how allpass substitution could work.
Yet this particular filter is i guess more difficult to do like this due to the triple output..

[Tepeix]

Find some way to calculate the 4 values..

Yet it's not perfect.. When close to nyquiest the resonance decrease, and the level of Bp Hp deviate a little..
Also the level of Hp deviate when res is high...

It might be possible to adjust increasing Q, But at nyquiest there's no more resonance..
This is indeed a big difference against true ZDF !..
But, the true decrease happen so late that if increasing Q it might be not audible..

What is cool is that for now the 4 values are not so difficult to get..

[Tepeix]

Find a way to better normalize Bp and Hp..
That's easy, lvBp = 1-(q1*4) LvHp = 1+(q2*4)

Now testing with lfo this seams very stable.
But maybe sounding strange ?? I have yet to compare. there's some strange resonance at some setting...

Now is it Zero Delay ? I'm not sure.. But if not might be very close except nyquiest..
Feedback coming from Bp and Hp, it's impossible to maintain resonance at the end..
But there's an optional fix that increase resonance close to it.
Might be possible using also the Lp..

Need to hear more comparison too..

[Tepeix]

Reading again, i think i understand more what you said Martin.

I was watching the frequency response, phase, thinking that a ZDF might have the exact same..
But they could also be the same with a non ZDF ?
Where the real attribute of ZDF is to make possible fast modulation, and also stay stable at low frequency ?

Normally the allpass substitution, (but i'm not always sure what i do is a legit one) would do this.
But using a feedback is maybe breaking this rule..
Yet, with some adjustment, the feedback will not cause much problem, but the difficulty become to get the same frequency response with allpass..

Yep there's also another way but i don't know how much legit..
Where the resonance is just an added bandpass... But would it really be the same ?..