bandwidth limited pulse,what window function is it?
From the great many types of window functions described on Wikipedia, the familiar rectangular window stand out has having a pretty small bandwidth. It's unfortunately also one with about the worst spectral leakage. 

Now for a given maximum allowable spectral leakage level, you might want to have a look at the Dolph–Chebyshev window, which minimize the norm of the side-lobes for a given main lobe width (or equivalently minimizes the main lobe width for a given maximum side-lobe level). Note however that this window has impulse like discontinuities at the edges in the time-domain due to the constant side-lobe level in the frequency-domain. These discontinuities are more significant for larger side-lobe level as can be seen in the following graph: