Hi,
Yes, it can affect the spectrum. I don't really know a good source that goes into full detail. Mike Donahue talks a bit about it here:
https://youtu.be/_ONM6f_IW-c?t=729Depending on your excitation, you need to worry about things like aliasing, or normalizing depending on where the excitation delivers the power. (One benefit of a sinc pulse is that it is flat in fourier-space. ie, it excites all modes equally. Other types of excitations might preferentially excite particular frequencies/modes, etc, that you need to worry about).
Best,
Josh L.