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Assume our signal source has a white background noise. The output of this source is connected to our system. We know that increasing the input bandwidth of the system leads to more noise flowing into the system and hence higher noise power.

Is there any way to somehow decouple the input bandwidth of the system and the noise power fed into the system, so that the power of the noise would be independent of the input bandwidth of the system seen by the source?

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  • \$\begingroup\$ If you figure this out, a lot of people will want to talk with you because that would be some amazing technology. \$\endgroup\$ – Joren Vaes Jun 2 '17 at 15:01
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    \$\begingroup\$ You could make an amplifier that contributes so much noise of its own that the noise from the source is insignificant. \$\endgroup\$ – The Photon Jun 2 '17 at 15:32
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Is there any way to somehow decouple the input bandwidth of the system and the noise power fed into the system, so that the power of the noise would be independent of the input bandwidth of the system seen by the source?

Yes, it's called filtering and specifically low pass filtering. However, if you want to measure valid signal frequencies above the filter cut-off you have a problem - noise is filtered just the same way as signals.

On the other hand, if you know your signal frequency then you can build a filter that tightly hugs that frequency and, to a reasonably large extent, removes noise except that which is in the pass-band of that filter.

This is how a radio receiver operates - it filters the input to just the approximate bandwidth of the modulated signal and all other noise is fairly well excluded. It's most noticeable on radio receivers that quote a sensitivity figure (usually around -90 dBm). If the radio has a tighter bandwidth, that figure can easily be in excess of -110 dBm because the filtering can be much tighter.

Of course, if you can freeze the signal source (and the noise previously produced was thermal in nature) then this can help a lot but you might not be keen on a bunch of helium or nitrogen tanks lying around.

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Hah, I was going to leave a note about white noise having equal noise power for each unit of bandwidth.

But, if you have a 1/f noise source, and look at the noise with a constant Q band pass filter. You will find that the noise remains constant as you lower the frequency of the filter. (As you lower the frequency the band width also reduces.) So here is a (contrived) case where you can change bandwidth and keep the noise power constant.

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