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:

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

to ${\frac {a}{f}}$

Where $Td$ is the time between measurements, $s=i\cdot 2\pi f$, and $a$ has the units of ${\frac {watts}{hz}}$ 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:

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

References

• Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972. (See Chapter 5)
  • (Section 5.2, Sine and Cosine Integrals)