I present an approach which determines analytically, for any desired output Gaussian pulse-envelope modulated chirped harmonic wave of arbitrary width at a given propagation distance in an absorptive, dispersive linear metamaterial medium acting as a compressor, the required, specific input pulse modulated wave. Employed asymptotic techniques yield the analytic description of the dynamical evolution of the appropriate input wave which is time-focused, and dispersion compensated upon propagation in a linear time-invariant system with a transfer function representing a chosen, physically realizable, Lorentz-type metamaterial. This approach is validated upon comparison with the results of different employed numerical experiments.