Different questions lead to different answers:
-- Equation [1] describes the current in the resistor, whereas
-- I was looking at the voltage across the capacitor.
One dead giveaway: Look at the asymptotes. For my filter,
the square of the voltage gain goes to unity at low frequencies,
and falls off in proportion to 1/f^4 at high frequencies.
Equation [1] does neither of those things.
As remarked previously, data visualization helps a lot.
It's not just for experimental data; it also helps
make sense of theoretical calculations.
Tangential remark: Equation [1] could also be thought of
as the voltage across the ideal (noiseless) part of the
resistor, but since that is unobservable, this interpretation
is not the best.
A small suggestion: For today it doesn't matter, but in
the future, in equation [1], it might be better to write
the LHS as G /squared/. It is more conventional to
reserve G for the /voltage/ gain. Today we happen to
be most directly interested in the square of the voltage
gain, but in other situations the voltage gain itself is
of tremendous interest, and G is the conventional symbol
for that. There is always temptation to redefine symbols
so as to streamline the notation, but such streamlining
risks sowing confusion.