First a method is presented to define a wavelet-based time-dependent spectrum for arbitrary non-stationary processes. Numerical results, assessed in terms of statistics depending on the spectral moments, prove satisfactory. Then the method is used to estimate the time-dependent spectrum of single-degree-of-freedom linear systems, in conjunction with an approximate analytical relation between the input and the output wavelet transform, already available in the literature. The validity of such relation is found to depend on the system and the input parameters. Interesting applications are feasible for linear systems with viscous dampers, subjected to seismic input
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