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. 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 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. The only issue that I can think of is the SNR.
