User:Rrogers314

For measurements the interest is in the "drift" of a variable with respect to a measurement at a previous time. This is calculated by applying the signal time differencing:

$1-e^\{-Td\backslash cdot\; s\}$

to

$\backslash frac\{a\}\{f\}$

Where $Td$ is the time between measurements, $s=i\backslash cdot2\backslash pi\; f$, and

$a$ has the units of $\backslash frac\{watts\}\{hz\}$ at 1 hz and includes the

contribution of both positive and negative frequency terms.

After some manipulation, the variance of the voltage difference in watts is:

$2a\backslash int\_\{0\}^\{f\_\{h\}\}\backslash frac\{1-cos(Td\backslash cdot2\backslash pi\; f)\}\{f\}df=-2a\backslash cdot\; Cin(Td\backslash cdot2\backslash pi\; f\_\{h\})$