  The spectral properties of a set of local gauge (BRST) invariant composite
operators are investigated in the $SU(2)$ Yang--Mills--Higgs model with a
single Higgs field in the fundamental representation, quantized in the 't Hooft
$R_{\xi}$-gauge. These operators can be thought of as a BRST invariant version
of the elementary fields of the theory, the Higgs and gauge fields, with which
they share a gauge independent pole mass. The two-point correlation functions
of both BRST invariant composite operators and elementary fields, as well as
their spectral functions, are investigated at one-loop order. It is shown that
the spectral functions of the elementary fields suffer from a strong unphysical
dependence from the gauge parameter $\xi$, and can even exhibit positivity
violating behaviour. In contrast, the BRST invariant local operators exhibit a
well defined positive spectral density.
