Suppose I have a window function $h$. If I specify the bandwidth for $h$ to be $c>0$, so $\text{supp}(h) \subset [-c/2,c/2]$, then what and when can I say about the support of the Fourier transform $\widehat{h}$?
Similarly, the other way around, if I have $\text{supp}(\widehat{h}) \subset [-c/2,c/2]$, then what and when can I say about the support of $h$ itself?
I know that the uncertainty principle would say that smaller support in the time domain will give larger support in the frequency domain and vice versa, but how can I find this relation explicitly?