Could you explain a bit about the relationship between locality and uncertainty in Fourier pairs? Many pages talk about uncertainty principle stating that the precision at which we can measure time duration of signal cannot unlimitedly grow without affecting precision on bandwidth. Many other pages talk about the lower bound on time duration and bandwidth product themselves, not uncertainties about them. What's exactly the link between them?
Furthermore, does the uncertainty principle forbid signal with unlimited time and bandwidth? I am talking about effective duration and effective bandwidth.
EDIT: trying to understand this principle using common sense from fourier scaling rules, I cannot guess why this is a lower bound instead of a theta bound..