Maybe a example of coupling effect in frequency modulated continuous (FMCW) radar will be helpful to better demonstrate my problem.
Let us consider a FMCW radar system. We have a complex transmitted signal $\textbf{x}(t)$ with bandwidth $B=50 \, \textbf{MHz}$, and duration time $T=7.3 \, \mu s$ of a chirp and $N=1024$ snapshots for a chirp, which leads to around $140 \textbf{MHz}$ sampling frequency, where $f_s=N/T=1024/(7.3*10^{-6})\approx 140 \textbf{MHz}$. For the considered bandwidth, we have simulated a coupling coefficient at $1 \, \textbf{MHz}$ interval. Then we want to model the time domain coupling signal at the receiver with considering those frequency response from ANSYS HFSS at $1 \, \textbf{MHz}$ interval within the bandwidth. How should we achieve it?
Suppose we have a complex linear frequency modulated signal $\textbf{x}(t)$ with bandwidth $B$ and duration time $T$. We sample this signal with sampling rate $f_s\gt B$, then we have the sampled version of this signal $\textbf{x}(n)\in\mathbb{C}^{1\times N}$, where $N$ is the number of snapshots.
Then if for $M\,(M\lt N)$ different considered frequencies within the bandwidth, we have a frequency dependent effect on $\textbf{x}$, which is $$\textbf{y}_m=H(m)\textbf{x}_m,\, m=1,\cdots, M $$ where $H(m)$ is the coefficient for the effect on that frequency. So how to peroform this frequency-depent effect on $M$ considered frequencies, then achieve the corresponding time domain signal after this frequency-dependent effect?