I'm recently encountering such a problem, which I think is very intuitive but I have no background knowledge on this field:

Given a signal with certain frequency distribution, e.g. we know that the signal has only high frequency part, we can expect that the number of zero-crossings of the signal has to be large. Is there a way to quantify this statement? For example, Can we give a (deterministic or stochastic) lower bound on the zero-crossings?

Thanks a lot for any hint or reference.