I got a simple modulating signal $x(t)=\sin(2\pi\alpha t)\sin(2 \pi \beta t)$ with carrier frequency $\alpha$ and modulation frequency $\beta$. The spectral correlation will obviously have components at the zero modulation frequency ($\beta = 0$). This is not surprising as the envelope signal is always positive.

I am aware that components at $\beta = 0$ also represent the average energy of the signal (Welch) but in the means of components separation/energy conservation, I would like to have the energy of $x(t)$ concentrated at $S_x(\alpha, \beta)$ only.

What am I missing here?

For the current case, do I have a complete separation between the two components having the same carrier and different modulation frequencies?
To me, it seems that part of the energy "leaks" to the zero modulation frequency component.

  • $\begingroup$ I might not be familiar with your terminology: could you define what $\beta$ means? Is $x$ a sinusoidal with that frequency, which gets mixed up to a frequency $\alpha$? $\endgroup$ – Marcus Müller Aug 11 '19 at 15:48
  • $\begingroup$ Edited the question... $\endgroup$ – Gideon Genadi Kogan Aug 12 '19 at 1:48
  • $\begingroup$ @MarcusMüller, do you find the edition helpful? $\endgroup$ – Gideon Genadi Kogan Aug 12 '19 at 11:43

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