Hi all,

Been using PD for a little while for making MobMuPlat patches.
While the filters found in pd extended are certainly good, I am looking for a higher order filter (LP and HP) this time. Preferably, an 8th order filter.

It is a requirement to use pd-extended only, for keeping MobMuPlat support.
The filters are required to have a cutoff input and a resonance input (neither needs to be audio signal in, but that would be a nice bonus).

While I did manage to get a patch working using rifft~ and basically graphing the desired frequency spectrum, the result isn't very great and probably adds unnecessary overhead.

Does anyone know of a freely available patch for these filters?
Or perhaps pointers on how to use the pole~ objects, so that I can create it myself?

Thanks in advance.

@manuels The moog is nothing special here just a standard cascaded filter. What do you think about this?

Which also should solve @elwinbran's issue and I had completely spaced out until you got my neglected filter theory working again, higher order VCFs generally put the feedback around only part of the filter and even a few lower VCFs did this. As you steepen the filter you change the frequency which has the proper cumulative phase alignment.

Edit: Out of curiosity I pulled out the Blofeld to see how they deal with this in hardware, the displayed filter cutoff is actually the frequency which the filter oscillates at and not the usual cutoff point. I wanted to also test this on the Micron which has an 8pole filter but it has some quirks regarding getting its filters to self oscillate and I don't seem to quite recall what they are at this moment or it might just be that not all of its filters can self oscillate, scrolling through my patches it seems I never use oscillating filters on that synth.

Another Edit: The Blofeld could actually be using a 2-pole resonance loop on the 4-pole filter, I tested by seeing if the frequency was the same between the two which I now realize is flawed. How the sound changed makes me suspect this is not the case and I was correct, I will do a more proper test later and maybe figure out the Micron, this got me curious.

@oid That's kind of what I would have expected. In the 4-pole version you shouldn't have a delay at all (or at least a much smaller one), and in the lower order filters the 64 sample delay is either too big or too small to produce the required phase shift ...

Which led me to the following idea: Couldn't we calculate the exact cumulative phase shift of the [lop~] filters and add a variable delay to get the required 180 degrees (or pi radians)? I found the formula for the frequency response in Julius O. Smith's book on digital filters and just tried:

resonance-fix.pd

To my surprise it really seems to work!

Interestingly the delay of the 4-pole filter shouldn't be as small as possible (as I thought) but depend on the actual cut-off frequency. The reason for that (if I understand correctly) is that the phase shift of the one-pole filter at the cut-off frequency actually seems to be somewhat less than 45 degrees.

Likewise, the Q value for self-oscillation (> 4) also seems to be an approximation. I scaled it to 1 by using the calculated amplitude response.

Edit FYI: Smith's one-pole filter analysis

Another edit: The deviation from the expected 45 degree phase shift depends on the sample rate, and in fact seems to be proportional to the sampling interval.

@manuels The 2x4 pole 'moog filter approximation' does seem to provide pretty good results. Had to fix the patch a bit, cause of compatability with extended, but it does have a good resonance.

As for your more recent message, it will take me a bit more time to fix the resonance fix patch, but I assume then that I can take that design and scale it up to more poles?

Also @oid thanks for the contribution, I think Im learning a lot here.

@elwinbran said:

As for your more recent message, it will take me a bit more time to fix the resonance fix patch, but I assume then that I can take that design and scale it up to more poles?

I don't think that's possible, four poles is the maximum here. But considering what @oid said about higher order VCFs, you could put the feedback path around only part of the cascade. I didn't think about this possibility earlier. So maybe it's better to have only one feedback path in the 2x4 pole filter? I don't have any experience with this kind of digital filter design and you should keep in mind that it's highly unconventional! Better you don't tell anybody that it's supposed to sound like a Moog filter or something.

Here's another way to fix the resonance frequency of the 4-pole filter:

resonance-fix-rzero.pd

In my previous attempt I calculated the required delay for the 180 degree phase shift, and it turned out to be around 3 samples for a wide range of cut-off frequencies. So introducing 4 averaging filters (or replacing each one-pole filter by a one-pole one-zero lowpass filter) reduces the optimal delay to around 1 sample, which is the smallest possible dalay anyway. Not tested yet, but it might be an alternative.

@manuels The compensation is interesting and I have been playing with it for the past couple days. Sort of a double edged sword, with the compensation I find it much more difficult to get a dynamic sound full of character and nuance that I seek but the resonance is much easier to deal with. Need to read more of Smith's filter book and understand things better so I can find the balance. One of these days I will learn to speak digital above the level of logic gates but the failures of my analogies seem to largely be useful and productive at least.

@oid Not sure where the "character" in your filter with extra delay comes from ... It's probably some kind of distortion. To recreate this effect in a more controllable way you could set the resonance frequency to some percentage of the cut-off frequency, like this:

resonance-fix-extended.pd

For values smaller than 100 the resonance is somehow distorted. Try feeding the filter with impulses at high resonance to hear the effect more clearly.

I removed the arctangent, so there isn't any nonlinearity in the feedback loop, just the [clip~ -1 1].

Edit: Would it be more reasonable to set the cut-off frequency to a percentage of the resonant frequency instead? I'm not sure ...

@manuels It is mostly an issue of the amplitude compensation, my filters have a great many sources of distortion, that compounding of error inherent in analog filters that I mentioned earlier, finding it difficult to maintain the same balance as without it.

Edit: The issue is to make it play well with all my other abstractions without functionally undoing the compensation or reworking all of my abstractions and patches to work with the new range. I am trying to have my cake and eat it too, which I do not think I can.

Thanks a lot @manuels, I guess I either have to take a 4 pole for granted or go with rfft~

More off-topic, I don't know what setting I may have that causes this, but even your extended compatible patch refuses to output any sound until I convert the cutoff signal to a float for the four lop~ objects.

@elwinbran Signal rate control input just came to [lop~] in the last release or so and I do not think [inlet~] passed floats back in the extended days either, don't quite recall on that one. Just replace that [inlet~] with the message rate [inlet] and stick to message rate for cutoff.