  A detailed analysis of the lowest two moments of the $\phi$ meson spectral
function in vacuum and nuclear matter is performed. The consistency is examined
between the constraints derived from finite energy QCD sum rules and the
spectra computed within an improved vector dominance model, incorporating the
coupling of kanonic degrees of freedom with the bare $\phi$ meson. In the
vacuum, recent accurate measurements of the $e^+ e^- \to K^+ K^-$ cross section
allow us to determine the spectral function with high precision. In nuclear
matter, the modification of the spectral function can be described by the
interactions of the kaons from $\phi \rightarrow K\bar{K}$ with the surrounding
nuclear medium. This leads primarily to a strong broadening and an asymmetric
deformation of the $\phi$ meson peak structure. We confirm that, both in vacuum
and nuclear matter, the zeroth and first moments of the corresponding spectral
functions satisfy the requirements of the finite energy sum rules to a
remarkable degree of accuracy. Limits on the strangeness sigma term of the
nucleon are examined in this context. Applying our results to the second moment
of the spectrum, we furthermore discuss constraints on four-quark condensates
and the validity of the commonly used ground state saturation approximation.
