Assume there is a band of noises that you you want to filter with center frequency Fn. Then The complex voltage representing noise at frequency F is V_(F, T) = V(F) e^(i W(F) T), where V(F) is the peak value of the sinusoidal voltage and W(F) is the angular frequency = 2 pi F, and T is time. I went ahead and LaTeXified this to be more readable:
If this voltage were applied to a bypass capacitor C, then
is the current through C that associated with the noise voltage at that frequency. This is valid for complex voltage and current since we already know that i = C dv/dt in real quantities, but
After some math we see that there's a corresponding complex equation for every real equation involving linear combinations of derivatives of voltage and current. I'm not so much interested in making this rigorous as figuring out now how to calculate the best value for C if it even matters.
Let me know if I can clarify anything.