  We study strictly hyperbolic partial differential operators of second order
with non-smooth coefficients. After modelling them as semiclassical Colombeau
equations of log-type we provide a factorization procedure on some
time-space-frequency domain. As a result the operator is written as a product
of two semiclassical first-order constituents of log-type which approximates
the modelled operator microlocally at infinite points. We then present a
diagonalization method so that microlocally at infinity the governing equation
is equal to a coupled system of two semiclassical first-order strictly
hyperbolic pseudodifferential equations. Furthermore we compute the coupling
effect. We close with some remarks on the results and future directions.
