"Don't window a transient signal"
To build on Laurent's answer, here is an example.  Top frame shows an example transient signal: a damped sine wave.  As the signal decays very quickly, the first 0.1s of the signal is the most interesting.  Second frame shows hann window.  Hann window is almost zero over that first 0.1s.  Third frame shows what happens when you apply hann window to the signal, the most interesting part of it is completely thrown away.