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A signal with PSD \$S_x(\omega)\$ is passed through a channel with frequency response \$H_1(\omega)\$ and at the receiver, it is passed through an equalizer with frequency response \$H_2(\omega)\$. The PSD for AWGN is No/2. My question is, does channel frequency response affect PSD of noise? For e.g. output PSD of signal here is $$S_x(\omega)\cdot |H_1(\omega)|^2 \cdot |H_2(\omega)|^2$$

but what about output PSD of noise, will it be No/2 \$|H_1(\omega)|^2\cdot |H_2(\omega)|^2\$ or only equalizer will change noise PSD to No/2 \$|H_2(\omega)|^2\$?

I encountered a question where they considered only equalizer frequency response to get output PSD of noise. Please help.

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The channel cannot magically distinguish between a signal and noise, so the frequency response H1 applies always.

Of course, if the source of the white noise is inside the receiver, and the noise does not pass through the channel, then the channel response is irrelevant.

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