Let's assume that I have some particular signal on the finite time interval which is described by function $f(t)$. It could be, for instance, a rectangular pulse with amplitude $a$ and period T; Gauss function with $\sigma$ and $a$ or something else.
Now I need to generate a signal which consists from randomly appearing functions $f(t)$ with random parameters (random parameters should be random in some specified range). If $f(t)$ is a rectangular function, the generated signal should consist from randomly generated rectangles appearing on random moments of time (rectangles should not overlap). Can anyone suggest what is the best way to do it in Mathematica?