I didn't end up doing graphics. Instead I figured out what the oscillators on VX-1's synthesizer, "AUD1", will behave like. The problem is that I wanted to have weird, colorful oscillators that may alias a lot - dropout distortions like the Atari 8-bits, chaotic functions, etc. - and so I can't just assume the input signal is good and work with it directly.
So I worked on making a cleanup strategy for naive oscillators that makes some compromises between anti-aliasing, high frequency preservation, and processing time.
For each output sample, I do this 4x:
1.5x oversample the original function with (osc(z) + osc(z + 0.5)) * 0.5
(This is actually a tricky simplification of using a "real" FIR filter kernel which relies on most of the terms cancelling out at the midpoint)
Run the resulting sample into my old IIR filter design, using the same 1.5x oversampling trick with (last filter input + this filter input) * 0.5. The IIR maxes out at samplerate / 2.5, which gives some additional headroom beneath the Nyquist frequency. Cutoff control of some kind will exist, possibly chained to amplitude control.
Output the final low-passed sample of the IIR.
It still aliases, you can hear it alias in the attached demo in the upper ranges. But the bulk of the signal is clear enough, which is what I'm aiming for, and while heavier oversampling improves it, the 4x/1.5x/1.5x strategy is "good enough" to work in a mix, especially as the filter cutoff dips lower.
The plan as of right now is to take this design, build 16 oscillator types around it(primitive functions, various noise/distortions, some fun/interesting stuff), a reverb and delay effect, and then some simplified amplitude and filter control. A key design goal is that the "knobs" on this have low granularity everywhere - there are exactly 256 pitches available, 16 volume steps, etc. It's inspired from early 80's chip sounds, but then will add things that give it optional shimmer and polish and make it a chameleon of an instrument.
I might even add some kind of lo-fi PCM.
