How to process a signal in frequency domain then convert it bakc to time domain?

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?

• you already tag with fft and ifft, so I'll presume you're familiar with the DFT — as long as your frequencies divide $B$, that's the solution right there. Commented Mar 22, 2023 at 10:34
• Also, your example on top is in direct contradiction to your question below: Question says $f_s =B$, the example says $f_s \gg B$; so, which is it? Commented Mar 22, 2023 at 10:35
• @MarcusMüller Sorry for not modifying the question below. I have now srt $f_s \gt B$. Commented Mar 22, 2023 at 11:21
• Please clarify by editing, not in comments. Also, it's not clear to me how you arrived at 139 MHz as sampling rate, that does not arise from your requirements. Please edit your question to clarify that, as well. Commented Mar 22, 2023 at 11:35
• OK, I will edit to clarify. Commented Mar 22, 2023 at 11:38

It takes a signal in the time domain x(t) discretizes it and return its frequency response which creates the baseband signal for the input of the modulator.The baseband signal isnt ready for transmission it is very lossy so the modulator raises its frequency and makes it a bandpass signal at some centered frequency $$f_{c}$$.Then it can be transmitted.The demodulator takes the received signal , creates the baseband out of it and sends it for signal processing.During signal processing the discrete time signal ,which is encoded in the demodulated baseband signal is extracted and the receiver can finally hear the music...