For now I use FFT to analyze the response of an electrical system to some transient signal. The transient signal is $x(t)$, which translates to $X(w)$ in the frequency domain. On the other hand I have $H(w)$, the response of my system to a unit input signal. Then to get the response of the system to the input $X(w)$ I simply do $X(w)*H(w)$; I then get $Y(w)$ and finally $y(t)$ follows from IFFT.
My question is, would wavelet be a better way of doing this? I know that wavelet analysis is usually very good for transient signal analysis, but I wonder if they apply when one want to get the response of a system to an transient input?