The TS-808 is a software emulation of the Roland TR-808.
The TR-808 service notes provide full schematics for each voice. I used them to make SPICE simulations of the circuits. I also analysed the best samples I could find (The Tape808, by Goldbaby), and tweaked the sounds until the waveforms and spectral content were as close as possible to the real thing. Most of the voices have more parameters and a greater range than their hardware predecessor.