Output based on the rate of change in the input voltage?

[Videographics]

Does anyone know of any Eurorack modules that can output a voltage based on the rate of change in an input voltage? I can imagine all sorts of uses for such a thing.

This inquiry is somewhat inspired by Expressive E’s crazy cool new Arché collection of virtual instrument plug-ins (https://www.expressivee.com/arche-collection) which translate the rate of change happening in a control input to the amount of movement for a virtual bow in a physically modeled bowed string instrument. Genius!

I was also thinking about it as I was looking at Ladik’s J-110 Derivator module which (with its Move output) can produce a gate when the input voltage is in flux, but doesn’t output a voltage relative to the rate of change.

Ideas? Thoughts?

[euromorcego]

what you want is a differentiator. Something that outputs a voltage that is proportional to the rate of change of an input signal.

there was a (short) thread about it that referred to this text:
https://www.allaboutcircuits.com/textbo ... -circuits/


The circuit doesn't look overly complicated. No clue if a module exists that implements such a function.

ps. I assume such circuits play a role in quadrature oscillators and look useful for waveshaping. It is also essentially a high-pass filter.

[Videographics]

what you want is a differentiator. Something that outputs a voltage that is proportional to the rate of change of an input signal.

Thanks for the quick response! Shakmat says their SumDif is a differentiator but it doesn’t appear to do what we’re talking about. Am I wrong? Is a differentiator really as simple as a mid-side processor or are different types of differentiators?

https://www.modulargrid.net/e/shakmat-modular-sumdif

[moremagic]

a differentiator would be a high pass filter. youd want one at cv rates presumably, so you could use a VCFQ in LF mode or send it to a slew, then inver it and sum it with the unslewed signal

[Videographics]

there was a (short) thread about it that referred to this text:
https://www.allaboutcircuits.com/textbo ... -circuits/

The circuit doesn't look overly complicated. No clue if a module exists that implements such a function.

This certainly makes it look simple enough. But that only adds to the mystery of why we don’t see them anywhere. And if they appear to be super useful and so closely related to integrators (slew generators, slew liters, function generators, etc.) which we have way too many of, where are all the differentiators?!

[Sunden]

You could hack a version with a shift register, a clock, a difference block (e.g. an attenuverting mixer), optionally a vca and a slew. We will only be calculating the average rate of change, not the derivative, but the faster our clock, the closer we will get.

let your signal that you want the slope of be called "x"

Plug the signal that you want the slope of into your shift register

Plug your clock into the shift register

Plug the first output of your shift register into your mixer at unity

Plug the second output of your shift register into your mixer at inverted unity.

The output of your mixer is now the difference between your signal at two points in time - you can scale them back down depending on your clock speed manually using the knobs, or:

If you patch the output to a vca, you can use a single offset to control both your clock speed and the gain of the vca - the faster the clock speed the higher the gain of the vca should be since you are approaching the instantaneous rate of change.

You can patch it to a slew to smooth out the staircasing.

[mskala]

Shakmat says their SumDif is a differentiator but it doesn’t appear to do what we’re talking about. Am I wrong? Is a differentiator really as simple as a mid-side processor or are different types of differentiators?

They're simply wrong. They are selling a voltage subtractor, and they don't know the word for that in English.

You could try a high-pass filter with the cutoff set low; for most audio purposes, that will provide results very similar to those of a true differentiator.

[Videographics]

Wow, thanks all! A high-pass filter works well for this only there’s a bit of a delayed response I’m still working on. Right now, if the voltage changes too quickly, I get nothing.

I tried it with a Dentrites filter set to 1-pole high-pass and it worked even without a voltage offset but the negative voltage offset helped to increase the effect. Note most filters will need some negative offset on the cutoff’s cv input to get the full effect.

The one thing I was imagining that’s different from how this works is that, if you feed it a falling voltage, you get a negative voltage out. So if you want any movement (up or down) to produce a positive voltage, you need to flip all the negatives with a rectifier.

Rediculous patch idea:
Grab a voltage offset and run it through a low pass filter and then into the cv in on a VCA. The VCA will only open when you’re actively turning the knob. So put some low frequency noise into the audio in of the VCA and the offset knob will make noise only when you move it — as if it were faulty and had gunk in it. Loads of fun!

[mskala]

Wow, thanks all! A high-pass filter works well for this only there’s a bit of a delayed response I’m still working on. Right now, if the voltage changes too quickly, I get nothing.

There will always be some delay. It's impossible to detect rate-of-change accurately without sampling over some nonzero period of time, because you need to see the voltage at one moment and then see it again at a later moment to know that it has changed. If you make the measurement time shorter, then the change in voltage that you have to measure is smaller for the same rate-of-change, so the accuracy at which you can measure voltages limits how short you can feasibly make the measurement time. This is another facet of the general trade-off between frequency and time accuracy that also applies to stuff like pitch shifters, as described here: https://northcoastsynthesis.com/news/fr ... ncertainty

However, differentiation is one of the easiest cases for this sort of thing and you can probably get the delay short enough not to be a problem, by pushing the cutoff of your high-pass filter very low.

The one thing I was imagining that’s different from how this works is that, if you feed it a falling voltage, you get a negative voltage out. So if you want any movement (up or down) to produce a positive voltage, you need to flip all the negatives with a rectifier.

That's the usual way for it to work mathematically, because differentiation is most useful in math when it's a linear operator: multiplying the input by any real number, including a negative number, multiplies the output by the same real number. You'd lose that property if the result of differentiation were always positive. But of course for audio purposes you're free to want some other behaviour, and in that case I think putting the high-pass output through a rectifier is probably the easiest way to go.

[Videographics]

Thanks mscala!!! Another super helpful reply. I understand the math is all logical enough. It sounds like if I can drive the filter frequency lower and massage the output response, I can probably make this work as sensitively as I was imagining. I’ll keep trying things along these lines...

[Cat-A-Tonic]

Interesting thread.

There is a (video rate) differentiator available from LZX (Sandin IP series).

I ought to try it processing voltages from the Sensory Translator / Audio Frequency Decoder (spectral envelope followers).