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In the system shown below, can white Gaussian noise amplify or attenuate the input signal? enter image description here

Most of the time we check signal level proportional to noise level (such as noise figure) not singly.

I have obtained PSD of my desire system's output and it is a combination of

  • a) Dc term

  • b) reaction of input noise to itself

  • c) reaction of input signal to itself

  • d) reaction of input signal and input noise.

At system's output at frequency $\omega$ should I assume terms (c) and (d) as the signal level? Or c is enough?

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    $\begingroup$ I'm not sure exactly what you're asking, but it sounds like you're asking if there are situations where you might add noise to a signal before it is input to a nonlinear device. The answer is yes; this technique is called dithering, and can be used to turn what would be deterministic quantization errors in an ADC (resulting in discrete spectral artifacts) into random errors, flattening the quantization noise spectrum. $\endgroup$ – Jason R Aug 31 '16 at 11:21
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    $\begingroup$ Dithering is a specific example of a more general idea - see stochastic resonance $\endgroup$ – David Aug 31 '16 at 12:55
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If the noise process has correlation with the input signal, then it is theoretically possible, no matter what kind of device you use.

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As Jason R. says in the comment, dither will do this. Another phrase to look for is noise shaping where the noise spectrum can be reshaped to not interfere with the signal of interest.

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