Here's a quick fork with one line, no noise, and an increasing-frequency sine wave: https://observablehq.com/d/ed17fc04bb7eb887
I suppose one can incorporate uncertainty on f(t) by having g(y,t) = gausy(0,\sigma(t)) * \delta(y-f(t)) (which would also effectively antialias in the few-lines case).
Also I guess you have to be careful not to plot a Weierstrass Function!