[sdiy] Time-varying all-pass filters

Rutger Vlek rutgervlek at gmail.com
Thu Jan 6 13:35:48 CET 2022

Thanks Mike!

Any specific design you could refer to?


Op do 6 jan. 2022 12:45 schreef Mike Bryant <mbryant at futurehorizons.com>:

> Hi Rutger
> If I understand you correctly then I think an analogue domain
> implementation does exist but in radio receivers.   Not sure how applicable
> they are to audio frequencies as the required frequency range is probably
> much wider but might be worth a look.
> Mike
> -----Original Message-----
> From: Synth-diy [mailto:synth-diy-bounces at synth-diy.org] On Behalf Of
> Rutger Vlek via Synth-diy
> Sent: 06 January 2022 10:04
> To: SDIY List
> Subject: [sdiy] Time-varying all-pass filters
> Dear list,
> In the last months I’ve been fantasising about a new mono synth (for
> personal use, nothing commercial), that could provide classic sounds, but
> also something slightly more original (at least for me). I’ve been reading
> a lot about FM/PM, about formant synthesis and pulse-forming, and about
> windowed-sync. I’ve done experiments with combinations of these on my Nord
> Modular G2 (digital) and found them musically really satisfying!
> So now I’m making small steps towards a first prototype of these ideas in
> analog. Originally, I planned to do a thru-zero triangle core oscillator,
> after I read older threads about how David Dixon and Bernie Hutchins
> implemented it, but felt the circuit complexity and potential impact on
> tuning stability was not really outweighing my limited use of FM/PM sounds.
> So, I decided to start looking for simpler ways to obtain some of the
> sounds characteristic of PM/FM, as well as the possibility to obtain
> sine-to-saw and sine-to-square waveshaping by means of self-modulation. Rob
> Hordijk made a nice implementation of this type of waveshaping in his
> OscHRM.
> Then it occurred to me that, assuming the input is a sine wave, a phase
> shifted version up to 180 degrees could be obtained from modulating an
> all-pass filter that is also tracking along with the pitch of the
> oscillator. The most important benefit of this approach is that the whole
> PM stuff becomes separated from the oscillator core, just like a wave
> shaper, and would guarantee stable tuning, even in cases of self-modulation
> (from the output of the all-pass filter back to it’s frequency input). So I
> prototyped it in my Nord Modular, and it works rather well! It’s not
> identical to true FM/PM, but provides sounds with very similar
> characteristics and allows for forms of self-modulation as well! When I
> searched the internet and archives of this list, I found the idea was not
> really new, and others have at least written about it.
> Then I moved to Spice modelling of an analog equivalent, and discovered
> something unexpected. Without modulation, the circuit operates at unity
> gain, preserving a sine wave of the same amplitude (10Vpp) as the input.
> However, depending on the modulation signal, excursions of up to 3 times
> this amplitude occur at the output. Going back to my Nord Modular, I
> realised the exact same thing is happening there, but the Nord’s headroom
> is sufficient to deal with it. So then I discovered that classic all-pass
> filter implementations do not generalise to time-varying applications….
> It turns out that there are special implementations for time-varying
> all-pass filters in the digital domain:
> https://www.researchgate.net/publication/3343262_Time-varying_generalizations_of_all-pass_filters.
> I have not been able to figure out if they exist (or can be designed along
> the same principles) in the analog domain. Does anyone have experience with
> this in analog? If not, I could consider designing for more headroom than I
> anticipated, or could try and soft-limit the output of the all-pass filter.
> Any suggestions or insights are appreciated!
> Rutger
> ps. Happy healthy new year!
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