  It has been observed that an interesting class of non-Gaussian stationary
processes is obtained when in the harmonics of a signal with random amplitudes
and phases, frequencies can also vary randomly. In the resulting models, the
statistical distribution of frequencies determines the process spectrum while
the distribution of amplitudes governs the process distributional properties.
Since decoupling the distributional and spectral properties can be advantageous
in applications, we thoroughly investigate a variety of properties exhibited by
these models. We extend previous work that represented processes as finite sum
of harmonics, by conveniently embedding them into the class of harmonizable
processes. Harmonics are integrated with respect to independently scattered
second order non-Gaussian random measures. The proposed approach provides with
a proper mathematical framework that allows to study spectral, distributional,
and ergodic properties. The mathematical elegance of these representations
avoids serious conceptual and technical difficulties with limiting behavior of
the models while at the same time facilitates derivation of their fundamental
properties. In particular, the multivariate distributions are obtained and the
asymptotic behavior of time averages is formally derived through the strong
ergodic theorem. Several deficiencies following from the previous approaches
are resolved and some of the results appearing in the literature are corrected
and extended. It is shown that due to the lack of ergodicity processes exhibit
an interesting property of non-trivial randomness remaining in the limit of
time averages. This feature maybe utilized to modelling signals observed in the
presence of influential and variable random factors.
