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.