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5

No. The aliased component will interfere with the non-aliased components and the interference can constructive or destructive. Trivial example: $$x[n] = \sin\left(\frac\pi2n\right)$$ If you down sample this to $y[n] = x[2n]$, you get all zeros.


0

The factor of "2" comes from the contribution of the negative frequencies, which doesn't apply to DC. A better way to plot this is to NOT multiply with 2 but plot the entire FFT range from -400Hz to +400Hz. There you will see three components: 1 W at DC and 0.25W each at -50Hz and +50Hz which is exactly what's happening here. If you want to plot ...


1

If the system described by the transfer function $H(s)$ is stable, you can obtain its frequency response by substituting $s=j\omega$, and use the relation that you found: $$S_Y(\omega)=S_X(\omega)\big|H(j\omega)\big|^2\tag{1}$$ where $S_X(\omega)$ and $S_Y(\omega)$ denote the power spectra of the system's input and its output, respectively.


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