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How can I simulate a lowpass filter sweep with a 4-bit, 32-sample programmable sound generator?

I'm trying to simulate a lowpass filter sweep on a sawtooth wave, with a touch of resonance, on a programmable sound generator. The PSG lets me create an unlimited number of arbitrary 4-bit, 32-sample waveforms. I can change waveforms every 16 milliseconds with no noticeable gap in between. Anybody know of a software application, or how even just how to do the math to calculate this filter sweep into a series of these 4-bit, 32-sample waveforms?

Obviously this isn't going to sound like a Moog :P I just want the filter sweep to sound....recognizable.

Whoever answers this best gets credit in a project I'm working on.