# Does excitation type matter in a time-domain simulation/computation of a transfer function of an LTI system?

Let's say I am running a FDTD simulation of a wave-equation to determine a transfer function of an LTI system:

\begin{equation} H(f) = \dfrac{Y(f)}{X(f)}\ \end{equation}

where $Y(f)$ and $X(f)$ are Fourier transforms of signals measured at some point in the FDTD grid for a grid with an "obstacle" inserted and an empty grid, respectively, due to an excitation $s(t)$. Assume that it's an acoustic wave simulation and that the "obstacle" is modelling a fully reflective object.

My question is: does the type of an excitation signal $s(t)$ matter in that kind of problem? For example, how broadband the signal is? And if does matter, then - how? My intuition tells me since in the end we're computing a relation of two signals, any propagation issues of the input signal will be the same in both simulations and therefore cancel each other in the above equation.

• What does LTI stands for? I don't think that the "propagation issues" are linear. – nicoguaro Sep 11 '17 at 14:25
• LTI = linear time invariant – sssssssssssss Sep 11 '17 at 17:46