Herein, we make use of a double-sided power spectral density defined on a whole range of frequencies, both negative and
positive, that yields the following connection to the variance of an arbitrary observable
:
It is
worth noting that in the GW community, the sensitivity of GW detectors as well as the individual noise sousces are usually
characterized by a single-sided power spectral density
, that is simply defined on positive frequencies
. The connection between these two is straightforward:
for
and
otherwise.