  A type of gravitational-wave signals in the LIGO-Virgo sensitivity band are
expected to be emitted by spinning asymmetric neutron stars, with rotational
frequencies that could plausibly emit continuous gravitational radiation in the
most sensitive band of the LIGO-Virgo detectors. The most important feature of
such kind of signals is in their phase evolution, which is stable over a long
observation run. When using analysis based on matched filtering, the phase
evolution of long-coherent signals is needed to define how to build a proper
template grid in order to gain the best signal-to-noise ratio possible. This
information is encoded in a matrix called \textit{phase metric}, which
characterizes the geometry for the likelihood given by the matched filtering.
Most of the times, the metric for long-coherent signals cannot be computed
anlaytically and even its numerical computation is not possible due to
numerical precision. In this paper we show a general phase decomposition
technique able to make the template metric analytically computable. We will
also show how this variables can be employed to distinguish in a robust way
among astrophysical signals and non-stationary noise artifacts that may affect
analysis pipelines.
