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:

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

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

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

$$2a\int_{0}^{f_{h}}\frac{1-cos(Td\cdot2\pi f)}{f}df=-2a\cdot Cin(Td\cdot2\pi f_{h})$$