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

Factorization of Second-order strictly hyperbolic operators with non-smooth coefficients and microlocal diagonalization