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Suppose I have a sensor which has a dominant white gaussian noise source, a \$1\textit{unit}/\sqrt{Hz}\$ noise density and a bandwidth of 100Hz. Then the noise becomes 10\$units\$. Is this a measure of the standard deviation of the noise? What exactly is \$10units\$ a measurement of?

In essence my question is, assuming a AWGN source with noise \$10units, \$ is it proper to say that this implies that the noise \$w \sim N(0,10^2)\$?

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  • \$\begingroup\$ I believe I am correct, and this answers my question \$\endgroup\$ – john morrison Jan 7 at 20:57
  • \$\begingroup\$ The 10 units is a measure of the RMS noise. \$\endgroup\$ – Spehro Pefhany Jan 7 at 21:00
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The RMS signal level for Gaussian white noise is measured in units per square root of bandwidth. And RMS has the same formula as when calculating the statistical standard deviation of a series of points. So, for instance;

For each point, calculate the distance from the mean value (call it 0 volts), square the distance. Repeat for all other points and sum all the squared distances. Then divide by the number of samples (take the mean of the squares) then, take the square root. Sound familiar?

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