  The interaction between the quantum vacuum and time-dependent boundaries can
produce particles via the dynamical Casimir effect. It is known that, for
asymmetric Casimir systems, there is an imbalance in the particle production on
either side of the boundary. Here, we consider a real massless scalar field in
1+1 dimensions interacting with a moving $\delta-\delta^{\prime}$ mirror with
time-dependent properties. The spectral distribution and particle creation rate
are computed, which now include an additional interference term that can affect
different parts of the spectrum in a constructive or destructive manner. The
asymmetry of the system is investigated by analyzing the difference in particle
spectra produced on the two sides of the mirror. Additionally, we also explore
enhancement of the spectrum and its asymmetry within the context of a
stationary $\delta-\delta^{\prime}$ mirror subject to multiple fluctuation
sources.
