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Is there some recommended way of fixing the power source noise issues?
The quick prototype in TFA is essentially a bunch of components connected together with long antennas, so literally any construction technique better than that will help...
You can emulate waveshapers with steeper aliasing falloff than 6dB/octave, using integration-based techniques to calculate the average output value of a waveshaper when interpolating multiple input points (or something like that). There's a paper describing various orders at http://dafx16.vutbr.cz/dafxpapers/20-DAFx-16_paper_41-PN.pdf (if I remember the right link, RIP it's not HTTPS).
This is a pretty complex build to throw together in such a short time, and it is super impressive

I could have sworn I saw Morton Subotnick performing with something like this back in the 80's (with Electric Phoenix, maybe?) but Googling is giving me nothing. Does this ring any bells for electronic music fans?

Reminds me of a fully-analogue approach to generate arbitary waveforms using a cardboard template stuck to the front of an oscilloscope. Basically, cut out the desired shape, stick it on the 'scope and point a photocell at the screen. The photocell drives the Y axis in a feedback loop so the spot height is a function of brightness -the idea being that the spot rides along the top of the template maintaining a constant brightness (with X timebase setting the output frequency - fairly obviously, needs an analogue 'scope with fully variable timebase).

Could probably do it with a flexible curve these days, to save on the scissors and cardboard.

> Hardware Reverse Oscilloscope 2

A hipster name for a frequency synthetiser. /s

Arbitrary waveform generator, actually.
When I look at the diagram I think, that this would be perfect introductory FPGA project. It is interactive, so it’s fun for the designer. Plus it touches digital signal processing and interface to external components. Such project is super cool compared to all other introductions I saw before.
harder to develop and ~6x more expensive (DE10-Nano vs teensy + pico)
You can get an UPduino for $30, that's probably plenty of FPGA for a project like this.
The sound of the synth was so much louder than his voice that the video gave me a low grade headache.