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 Forum index » Clavia Nord Modular » Nord Modular G2 Discussion
Resonant filters with "inverted feedback"
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extone



Joined: May 29, 2006
Posts: 4
Location: Australia

PostPosted: Wed Nov 28, 2007 3:38 pm    Post subject: Resonant filters with "inverted feedback" Reply with quote  Mark this post and the followings unread

Hey everyone, I was reading this thread about how to make resonant lowpass filters using inverted feedback with a mixer and the lowpass module:

http://electro-music.com/forum/topic-2143-0.html

I managed to create the resonant effect but I wondering how this actually happens. In the thread all that is mentioned is osc->mixer->filter->invert->back to mixer->output and you get resonace at the freq you set the filter to. But how is this happening? I am wondering particulary about how the inverter module plays its part.

I would have thought that an inverted signal being fed back into a mixer with the original would have canceld out freq's not increased them? obviously i'm getting mixed up somewhere.

I also noticed I got a rather nice resonant sound when I changed the inverted module from bipolar to polar.
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Blue Hell
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PostPosted: Wed Nov 28, 2007 4:08 pm    Post subject: Re: Resonant filters with "inverted feedback" Reply with quote  Mark this post and the followings unread

extone wrote:
I would have thought that an inverted signal being fed back into a mixer with the original would have canceld out freq's not increased them? obviously i'm getting mixed up somewhere.


No, this is correct and you're not getting mixed up. The filter itself does an inversion as well, although this depends on the filter type. When I do something like this I just try it with and without an inverter to see what happens.

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electroboz



Joined: Nov 29, 2006
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PostPosted: Wed Nov 28, 2007 4:09 pm    Post subject: Reply with quote  Mark this post and the followings unread

basically by feeding the ouput of a mixer (in the digital domain) back into itself you are creating a 1 sample delay. it is this delay or phase shift that keeps the feedback from canceling itself. this is explained in depth at robs site. http://www.xs4all.nl/~rhordijk/G2Pages/
scroll down to the sections on i"ntegration and lowpass filtering" and also the section on filters in general.
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Kassen
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PostPosted: Thu Nov 29, 2007 2:21 pm    Post subject: Re: Resonant filters with "inverted feedback" Reply with quote  Mark this post and the followings unread

Blue Hell wrote:
When I do something like this I just try it with and without an inverter to see what happens.


Funny, that's how I go about filter-design as well!
Laughing

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Stanley Pain



Joined: Sep 02, 2004
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PostPosted: Tue Dec 04, 2007 2:31 pm    Post subject: Reply with quote  Mark this post and the followings unread

Very Happy
now i understand...

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Fozzie



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PostPosted: Wed Dec 05, 2007 1:34 am    Post subject: Reply with quote  Mark this post and the followings unread

electroboz wrote:
basically by feeding the ouput of a mixer (in the digital domain) back into itself you are creating a 1 sample delay.


Well, there's certainly a delay, but not all filters have 1-sample delays (although you can surely make filters from fed-back mixers). Rob explains the issue clearly on his fantastic SynthesisWorkshops pages:

Quote:
In a resonant four-pole filter the poles are cascaded in series and the output signal at the end of the cascade is fed back to the input of the first pole to create a feedback loop. Feedback is very important as feedback is always necessary to create resonance. Each of the four poles will cause a very short delay on the signal. This delay is only 1/8th of the length of a single cycle of a waveform tuned to the pitch that is equal to the cutoff frequency of the filter pole. The four poles together will cause a total shift of four times 1/8th, so one half of this waveform cycle. If this delayed signal is additionally reversed in phase this ‘inversion’ will create an additional ‘phaseshift’ of another 180 degrees. This causes the delayed and inverted waveform at the output of the four poles to appear to have a delay of exactly a full cycle of the waveform, and so lag one cycle of the waveform behind in respect to the input signal. But note that it is only a sinewave component at a pitch that is equal to the cutoff frequency of the filter that will have this exact one cycle delay. Partials in the sound that are not at this cutoff frequency will have different phaseshifts. If the delayed and inverted signal is fed back to the input of the four poles it will reinforce the input signal and thus create the wanted resonance. In practice the input signal is mixed with the feedback signal before entering the first pole and output is taken from the output of the last pole. This will give a cutoff slope of 4 times 6dB, so 24dB. The resonance is defined by the amount of feedback. An important thing to remember in your experiments is that to make the filter resonant the feedback signal must always be inverted or phase reversed to be able to cause resonance, without this phase reversal the filter won’t resonate at all. This also applies when using two, three or more than four poles in your filter design.

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