I have a signal $x_1(t)$ with baseband bandwidth $W_1$ Hz over a carrier frequency $f_1$ and power $P_1$. I also have another signal $x_2(t)$ of baseband bandwidth $W_2$ Hz over a carrier frequency $f_2$ and power $P_2$. The carrier frequency $f_2$ is random, and thus part of $x_2(t)$ spectrum may overlap with that of $x_1(t)$. My question is: is there a simple mathematical way to calculate the power of the part of $x_2(t)$ that interferes with $x_1(t)$ in the frequency domain?

I know the power is the area under the power spectrum density (PSD) graph, but this requires knowing the PSD formula and do integration in software. Is there another simple mathematical way to do this?


1 Answer 1


No, there can't be a way, since "bandwidth" tells us nothing about how the power is distributed within that bandwidth.

Knowledge of that distribution is literally what a PSD is.

  • $\begingroup$ Thanks for confirming $\endgroup$ Oct 20, 2022 at 11:09
  • $\begingroup$ note that I'd say your question could have been easily answered by yourself, for example by making a drawing of a few possible spectra. $\endgroup$ Oct 20, 2022 at 11:09

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