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24dB/oct (4th order) HPF
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françois



Joined: Dec 23, 2006
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Location: Paris (France)
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PostPosted: Sat Dec 08, 2007 5:10 am    Post subject: 24dB/oct (4th order) HPF Reply with quote  Mark this post and the followings unread

Hello all,

I'm starting a new modular project, a very big one. It's just a project for now, and only on paper, so I can dream about how big I can make it. When the time comes to count how much money I have for it... I prefer not to think of it now.

Well, I want to have (at least) a Moog transistor ladder 4th order LPF. But a HPF is also useful sometimes. Up to now I've always been using two cascaded state variable 2nd order filters, not so bad, plus they don't need to be tuned to the same frequency and can have different resonance setings (quite little musical interest, but my musical talents are those of a mole).

So I thought, why not make a (poor man's) HPF for nearly free, by just subtracting the LPF's output from the original signal? I certainly have the schemo for Moog's HPF, but I have zigabytes of schemos, and I just wondered about a quick-and-dirty way of having an extra HPF.

I already see some potential problems. First, there may be a phase problem, the LPF introduces some phase shift, so simply subtracting may not work as expected. Second, when the LPF has resonance ("peak" in Moog parlance, "regeneration" on other synths), subtraction will result in an "anti-peak" in the HPF's response. Maybe that can be interesting...

I will do the maths for that and give it a try in simulation. But today is a rainy sad december day, and I don't feel like doing it just now...
If any of you has tried a similar thing, please let me know.

-- françois
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Fernando



Joined: Dec 30, 2006
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Location: Barcelona & Emporda, Spain

PostPosted: Sat Dec 08, 2007 6:27 am    Post subject: Reply with quote  Mark this post and the followings unread

Interesting project.

I have an schematic from Tom Gamble (EFM) describing a 4th order Moog HPF. But I can't recall if it was based on the original circuit or was a guess.
edit: it was a re-interpretation.

The Moog HPF is a pretty complex, discrete transistor one

Respect the substracting method (below): maybe it's not perfect but can yield interesting sounds and that's th epoint for me. Thank you for the samples

Last edited by Fernando on Sat Dec 08, 2007 1:33 pm; edited 1 time in total
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Dave Kendall



Joined: May 26, 2007
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PostPosted: Sat Dec 08, 2007 7:04 am    Post subject: Reply with quote  Mark this post and the followings unread

Quote:
So I thought, why not make a (poor man's) HPF for nearly free, by just subtracting the LPF's output from the original signal


I had a go at this a while ago. 2 things I noticed, firstly, matching the levels of the original and LPF was critical to achieve even partial phase cancellation (which gives the HPF effect.)
Also as soon as resonance was increased, the gain of the LPF signal changed, so the effect was lost.

It does work fairly well with no resonance, or a static resonance setting though, as the 2 samples show. I used a Yamaha digital mixer to try and avoid phase differences between the 2 signals being mixed. The VCF was in a Mutator LP VCF.

I did toy with the idea of using a pair of VCAs to try and get around this, so that when the resonance amount was changed using one VCA, the gain of the LPF signal was correspondingly decreased to compensate using the other VCA. I guess the response/performance of both VCAs would need to be very tightly matched and/or tweaked to get good cancellation.

It seemed like a lot of hassle in the end, so I shelved the idea........

If you do get any useful results, I'd be interested in hearing how you got on..... Smile

cheers,
Dave


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françois



Joined: Dec 23, 2006
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PostPosted: Sun Dec 09, 2007 2:26 am    Post subject: Reply with quote  Mark this post and the followings unread

Well... As I told, yesterday was a sad rainy december day, and I was not in the mood of doing math. But I got bored of playing sudoku, silly point'n'click games, or adding crazy symbols to my schematic drawing program. So I finally did the math.

Sorry, it seems uneasy to type formulas in this forum. I started with a standard Moog LPF with zero resonance, the transfer function being:
LPF(s) = 1/(1+s)^4 = 1 / (1 + 4s + 6s^2 + 4s^3 + s^4)
where s is the "reduced frequency", i.e. s = j.f/f0 with j²=-1 and f0 the tuning frequency of the filter. In France we use the letter p instead of s for some obscure reason...

Then the poor man's HPF's transfer function is:
HPF(s) = 1 - LPF(s) = (4s + 6s^2 + 4s^3 + s^4) / (same denominator as LPF)
while a "true" HPF would have:
HPF(s) = s^4 / (denominator)

Well, you do not even need to add resonance to see some problems. The "real" HPF has a single four-fold zero at s = 0, while the ersatz has four distinct poles at (1+s)^4 = 1, namely at s = 0, -2, -1+j and -1-j. In practice, that means that phase cancellation is at best of the domain of wish.

Things get even worse when you add resonance. I did a quick & dirty simulation with LTSpice (aka SwitcherCAD III) and all the phenomena Dave mentioned did occur. Although LTSpice can generate audio files, I don't think it is necessary to join any here...

So I will shelve this project, too. And build a true HPF, even if it's more complicated. It was planned anyway, but I hoped to get a "free" extra ancillary HPF... Too bad / sad. BTW, I'll also have a look at my "shelf", 'cause I have so many forgotten projects there, maybe some of them could be useful in some unexpected way !

-- françois
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yusynth



Joined: Nov 24, 2005
Posts: 1314
Location: France

PostPosted: Sun Dec 09, 2007 2:57 am    Post subject: Reply with quote  Mark this post and the followings unread

There is another somution that consists of injecting the signal (must very low impedance though) on the last stage of a moog ladder. Tom Gamble used this in the Wildcat and Osamu Hoshuyama provides a comprehensive explanation http://www5b.biglobe.ne.jp/~houshu/synth/Vcfv0212.GIF. I built an EFM Wildcat, and this quite works but ruins the LP filtering of the Moog ladder. Therefore I deactivated this option. IMHO this approach must be avoided.

Fernando wrote:
I have an schematic from Tom Gamble (EFM) describing a 4th order Moog HPF. But I can't recall if it was based on the original circuit or was a guess.
edit: it was a re-interpretation.

Yes it was and if the basic idea was fine the schematic contains some errors in some resistor values... I think the reinterpretation by Osamu Hoshuyama is more sensible :
http://www5b.biglobe.ne.jp/~houshu/synth/Vchp0302.GIF

François if you go for a 24dB/oct HP filter, you'd better try the Polyfusion HP VCF or even the Formant 24dB VCF.

Cheers

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Yves
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françois



Joined: Dec 23, 2006
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PostPosted: Sun Dec 09, 2007 3:11 am    Post subject: Reply with quote  Mark this post and the followings unread

Hello Yves, and thank you. BTW, I *love* your site ! Many excellent ideas there.

I agree with you that Osamu Hoshuyama's interpretation is more sensible, and clearer also. But anyway, I don't have real difficulties in designing a true 24dB/oct HPF, and I usually get a solution very similar to the Formant filter. I had more difficulties analyzing the Steiner VCF (although not too much).

My initial purpose was just to "tweak" the LPF to get an extra HPF, not very good, but useful for ancillary functions. It seems even that is not so sensible... Sad

-- françois
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yusynth



Joined: Nov 24, 2005
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PostPosted: Sun Dec 09, 2007 5:04 am    Post subject: Reply with quote  Mark this post and the followings unread

françois wrote:
My initial purpose was just to "tweak" the LPF to get an extra HPF, not very good, but useful for ancillary functions. It seems even that is not so sensible... Sad

Hi François

Well it was a logical approach but as you demonstrated yourself with the maths and I experienced it in a practical way and with SPICE simulation, it does not work as efficiently as expected...

I have another question though, are you needing a 24dB/octave high-pass response there because a mere 12dB/octave or even a 6dB/octave HP sounds more musical. However if your aim is pure electric sounds then a 24dB/octave is certainly worth it.

All the best

Yves

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françois



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PostPosted: Sun Dec 09, 2007 5:40 am    Post subject: Reply with quote  Mark this post and the followings unread

Hello again, Yves.

I don't know exactly why I need a 24dB HPF, or even if I need one at all. Most non-modular synths (or even semi-modular ones) don't have a HPF. The musical interest of it is probably not worth the hassle, except, as you notice, for purely "electrical" sounds.

But I want it for the sake of completeness. In fact what I am designing is an "Analogic Audio Computer", that is, an analog computer that works primarily in the audio range. I've been working a lot with analog computers, and loved it. The musical applications are the ludic part of the project.

In that setting, having all sorts of filters, voltage processors, and so on, is a necessity.

Yours,

-- françois
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yusynth



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PostPosted: Sun Dec 09, 2007 7:22 am    Post subject: Reply with quote  Mark this post and the followings unread

Well François, if you come from the world of analogue computer then what you need is state variable VCF (the same as the 2nd order differential equation solver), this way you get at the same time the low-pass, band-pass or high-pass responses.
Examples of this type of filter are numeraous : standard multimode VCF of the Formant, SEM VCF and so on.

BTW, HP filters are useful in synths don't worry Wink

Regards

Yves

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Dave Kendall



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PostPosted: Sun Dec 09, 2007 7:36 am    Post subject: Reply with quote  Mark this post and the followings unread

I'm with Yves on this one....
HPFs are often underestimated devices - they're also very useful in a mix - whether for electronic or other instruments, to control low-end from instruments that don't really need it - helping them sit much better in the mix.
A wee touch of HPF was my secret weapon for dialogue and interviews when I did a lot of sound dubbing and mixing for TV and corporate...... Smile

cheers,
Dave
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françois



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PostPosted: Sun Dec 09, 2007 7:37 am    Post subject: Reply with quote  Mark this post and the followings unread

Thanks Yves,

I do know the SVF, I've even built a couple of these. Actually I had some Formant modules when I was a student, and of course the two associated books.

-- françois
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prophei



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PostPosted: Sun Dec 09, 2007 9:23 am    Post subject: Reply with quote  Mark this post and the followings unread

françois wrote:
... Although LTSpice can generate audio files, I don't think it is necessary to join any here...


i am not very experienced with applications like this, and was wondering which are known to have actual audio output. are there specific technical descriptions of this feature that denote this ability in spice type software? i looked around for this kind of thing months ago, and could never figure out which apps would do it!

most seemed to never focus on anything audio in that respect. it seemed that actually hearing the output was not considered a priority..

thanks!

-michael
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frijitz



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PostPosted: Sun Dec 09, 2007 10:15 am    Post subject: Reply with quote  Mark this post and the followings unread

françois wrote:
I don't know exactly why I need a 24dB HPF, or even if I need one at all. Most non-modular synths (or even semi-modular ones) don't have a HPF. The musical interest of it is probably not worth the hassle, except, as you notice, for purely "electrical" sounds.

francois -- you might look into Scott Stites' version of Rene's version of the MS-20 filter. This can be switched between 1st order HP and 2nd order LP. I have built and am now playing with the proper dual to the LP (2nd order HP). See the thread here.

One possible reason for not needing a high-order LP is that the human ear-brain reconstructs missing fundamentals, so you still "hear" the lower components even if they are not present. Shocked

Very Happy

Ian
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françois



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PostPosted: Mon Dec 10, 2007 2:56 am    Post subject: Reply with quote  Mark this post and the followings unread

I do agree that a high-order HPF is useful in mixing. But does it need to be dynamically voltage controlled ? Anyway I want to have one, if only to experiment with it.

For now I'm reconsidering the "usual" SVF (one input, three outputs HPF, BPF & LPF) compared to the Steiner filter (three inputs HPF, BPF & LPF, and one output). The equations for the SVF are (in terms of Laplace transforms) :
BPF = s.LPF
HPF = s².LPF = s.BPF = IN - LPF - Q.BPF
where Q is the resonance factor. The input signal IN is injected into the input adder, which gives the HPF output. Why not inject it into the first or second integrator, thus creating a behaviour similar to a Steiner filter ? The maths are in favor of that...

BTW, if I want voltage controlled resonance (very easy to implement on a standard SVF), should it be linear or logarithmic ? Maths say it should be measured in dB (hence log), but e.g. the Formant SVF has a lin pot to control resonance. And I suspect that a 10-octave range (or 60dB) would be overkill for such a sensible parameter.

-- françois
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