Own oscillators and filters designs in a Synthesizer is a paradise for sound designers. No waveform or filter type limitation being exposed is a massive feature for a synth. In software until recently, the Linplug Spectral Synthesizer plugin could do this exactly. Still one of my favorite synth plugins but unfortunately the company no longer exist.
Designing own waveforms/filters in hardware is very rare but there were some. One of these was the Acxel, a super rare Synthesizer from the late 1980s manufactured by the Canadian company Technos.
Technos Acxel is based on additive synthesis: “the process of controlling a large bank of oscillators and amplifiers, ultimately combining them together to form complex timbres“.
Each voice of the Acxel features 32 oscillators and 33 amplifiers and offers a wide range of parameters to craft new sounds. Very different was the interface of the synth. With a LED matrix, you can draw waveforms directly on it with finger-tip.
Perfect Circuit Audio in LA has a unit for sale for very cheap $18999 USD and created for this occasion a very interesting walkthrough article and video about the Acxel.
More information here: Technos Acxel