Q: zero crossings and extrema of stationary Gaussian r.v.s
Here’s something new and exciting: let 
be a stationary Gaussian r.v.. Find the expected number of zero crossings in a unit interval. I’ll give you a hint: it can be expressed in terms of the second and zeroth moments of the signal’s spectrum. And I have no idea how to be about it 
If you get that one, try to show that the expected number of extrema in a unit interval can be expressed in terms of the fourth and zeroth spectral moments.
Possibly relevant posts:
- Spectral Mapping Theorem (6/14/2006)
- A cool problem in measure theory (4/9/2007)
- El Fin (9/28/2007)