phase rotator (aka 4 way allpass phase splitter [for cymbal synthesis])

there is currently a viral cymbal syntheisis video just uploaded to youtube that i am attempting to recreate in reaktor, but which has proven difficult

the method is ingenious and doing things with delay lines that i didn't know were possible. he starts with a simple karplus strong algorithm then adds allpass, vibrato, and phase distortion into the delay line to get something that sounds exactly like metallic excitation

the phase distortion and vibrato are trivial to implement with factory core modules but this "allpass" is something else entirely, while almost certainly being the key thing working on the sound to make it realistic

here is a link to the youtube video at the time we are interested in

the "allpass" used is a free plugin called Phase Nudge is definitely neither an 1p IIR allpass or a schroeder allpass. but upon further research it is almost certainly something called a phase rotator, which shifts all frequencies in a signal from 0 - 180 degrees, sort of in the way a hilbert transform shifts all the frequencies in a signal by 90 degrees

here is a link to a video showing the effect sweeping 1-180 degrees on a saw wave input

the video above has a time spectrogram showing an allpass response but the time domain response looking like some kind of very janky piecewise approximation of something like this:

a much smoother version of the same thing

which i have been able to implement 1/4 of easily in reaktor by crossfading between the outputs of the hilbert phase splitter in the factory library:

phase quartile.zip

so the question is directed at anyone who knows anything about generating the necessary coefficients for 4 allpass cascades generating phase shifted signals at 0 90 180 and -90. i've had a look at some of the maths inside the coefficient modules and they look pretty complicated 😑

however i believe this idea of hilbert style phase shifting/rotating inside delay lines has some real potential for stuff like physical modelling, and quite possibly at the bleeding edge

anyway not sure how active this forum is might tag some people depending k bye

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Studiowaves

Interesting that anyone would even think of doing it that way. My guess it all boils down to FM being created by phase shifting amplitudes and that in turn frequency modulates something else. You still need a seed for a starting point which in this case seems to be a sound sample. I think this is physical modelling of an object. What nice about this is (if it works) the ability to tap a cymbal and retap it while it is going just like a real cymbal. Samplers have never really cut the mustard of real cymbals and this would be a real work of art if it works. The only thing I know about all pass circuits as that they approach a 180 degree phase shift between the two start and end points but never really get there but it's safe to assume a maximum of 180 degrees is obtainable. I've never seen a 90 degree allpass filter unless it's 90 degrees between 2 points along the x axis. Is it possible? It seems safe to assume any number of all pass circuits can be cascaded for 180, 360, and so on so it might be better think in terms of radions. Whatever, if Fc is changed in successive cascade allpass stages you can derive many phase angles. So along all of this nonsense, I think it's cool to try it. I always thought you could crossfade a couple of cymbal samples and get fairly good results but nothing even close to something like this. Reaktor should have the capability to get this going, I'll probably just be an observer but I think you should start out with a bunch of core macro's that can be frequency modulated by another one. Something like the Cymbal ens. The question I have is what to use for the seed. What ticks it off? A burts, maybe a sample of the tick when it hits the cymbal.

The core cell is kind of a rudamental building block that uses FM on one input and the audio pass thru the audio. Something like this to get things on a roll. I think this might be a linear to log sweep of F.

Cymbal.ens

ANDREW221231

"I've never seen a 90 degree allpass filter"

that's what an allpass filter is, defined as 90 phase shift at cutoff for a 1p IIR

but yeah like you say, any configuration of allpass is still an allpass even some monstrous combination of four hundred of them. i tried using cascaded phase splitters, as in phase splitting both outputs of a phase splitter. it doesn't quite do the same thing as in the video but it seems to be in the ballpark? check it out. gotta go try this in a delay line now lolol

rotas.zip

errorsmith

"Phase Nudge is definitely neither an 1p IIR allpass or a schroeder allpass"

I think it is. Try send an impulse in it and look at the impulse response. It looks exactly like the impulse response of a schroeder allpass.

ANDREW221231

https://community.native-instruments.com/discussion/comment/249533#Comment_249533

i tried putting a schroeder allpass into a delay line and all i got was infinite ringing. but a schroeder does seem to behave pretty similarly to what the plugin does

ANDREW221231

i wonder if a schroeder could be adding some DC to the signal that's causing the ringing?

errorsmith

https://community.native-instruments.com/discussion/comment/249537#Comment_249537

Please upload an ensemble that showcases the ringing. So we can have a look. Just a feedback delay with an schroeder allpass in the feedback path.

ANDREW221231

https://community.native-instruments.com/discussion/comment/249539#Comment_249539

blow up.zip

here it is set with coefficients to quickly blow up but putting this together i discovered some settings that are more stable, but still not quite right

also here are the impulse responses of both, the left is schroeder in reaktor and right is the plugin. they look close but behave very differently within a feedback loop… but maybe it is just a matter of carefully tuning

errorsmith

There is a bug in your allpass. you added the z-1 delay at the wrong place. That made the allpass not spectrally flat causing the blow up. The correct place would be inserting it after the main delay of the allpass as if it is part of the main delay.

But i recommend deleting the z-1 and using the delays from the current library. the one that you are using is from an older library. The current ones are non solid (see the dashed line at the top and bottom). From their info: 'This delay can be used in feedback loops without causing an extra 1 sample delay.' They resolve the feedback internally without the need for z-1 delays. In the outer feedback you are using the new delay so the z-1 delay is not necessary there too so i recommend deleting it as well.

Attached is the corrected allpass. It uses the non interpolated delay 'Delay 0' to make the impulse response more clear. If you don't plan to modulate the allpass delay time you can leave it as it is. Otherwise use the interpolated delay (the one above 'Delay 0').

allpass.zip

ANDREW221231

https://community.native-instruments.com/discussion/comment/249566#Comment_249566

yeah that was one i pulled out of something from the UL dating back to reaktor 5 i believe lol. holy brilliant, thank you so much. we are back in the game. attached is the completed delay loop for the cymbal excitation section

cymbal.zip

silvermoats

rotas_continuous.ens

hey, not sure I understood the issue you were having with the original .ens posted correctly or whether you've resolved it since, but did you try just inverting the outputs of a single Hilbert phase split to complete a full rotation? I've attached a version with a continuous phasor here that seems to run pretty smoothly, though there might be a better way to code it manually I'm not thinking of.

it helps smooth between rotations if you use a sine or parabolic crossfade curve, I put a core adaptation of a scanner that does in as well, though you'll have to figure out a wrapping solution if you want to drive it with a single phasor.

interested in feature developments with this project for sure!

ANDREW221231

https://community.native-instruments.com/discussion/comment/249618#Comment_249618

yes thank you !! that was what i was going for but couldn't remember the configuration lol. also i was looking down the barrel of trying to build a core wave scanner so thank you for including that as well

here is the finished model with your module routed in as a switchable bypass. it works well in the delay line but seems to make the sound angrier or more gong like

cymbullB.zip

silvermoats

Nice, sounds pretty massive

Keep in mind you can also use the real and imaginary signals to extract the polar coordinates if you have a use for modulating the amplitude in addition to the phase. otherwise, you're basically just frequency shifting from scratch, which can be handy for flexibility but maybe less what you're going for

silvermoats

Although now that I look closer at it you probably just wanted manual control of the phase to change the feedback tone so it's probably not necessary to add anything else, just make sure you set the knob range to max out at 4 if you want the full rotation :)

Btw all due credit goes to the original creator of the core macro attributed in its description - I just dropped in the sine shapers to recreate the functionality of the primary version.

Studiowaves

Sounds promising. was tweaking cymbal. ens and got something similar to cymbal. Turned it up and when it clipped it sound more like a gunshot. the wife was a bitchin'. lol

I don't get the difference between one type of allpass to another. Don't they do the same thing?

This might help , put a spectum analyzer in the mix.

Cymbal2 with spectrum analyzer.ens

ANDREW221231

https://community.native-instruments.com/discussion/comment/249633#Comment_249633

had to try it because you never know with this stuff, i amplitude modulated the instantaneous phase giving something like waveshaping (since amplitude modulating the sine of instantaneous phase returns the imaginary output of the analytic signal). honestly cant tell whether i hear some more resonance in the higher harmonics or if i'm just imagining it

angry phase.zip

but having it in the delay line sounded pretty much identical to without it except for some pitch shift from the added group delay of the filters which is good to know an IIR allpass in a delay line can be fairly transparent. ive heard of using 1p allpass in delay lines to model stuff like string inharmonicity but i believe that requires some pretty careful tuning of coefficients

the phase rotator however seems to be doing something interesting. almost like something between pitch and frequency shifting in the range of a couple semitones. it definitely adds inharmonicity which is apparent when comparing back to back with karplus strong (the engage button in the following ens) but i can't tell how similar it is to frequency shifting because putting a frequency shifter into a delay line causes the signal to endlessly rise in frequency barber pole style!

karplus weak (2).zip

thinking about all this has made me realize that a short enough fft could also work in a delay line as well. much to think about

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