Time-Varying Spectra and Linear Transformation

One of the most important prerequisites for defining the spectrum of a nonstationary process is that the spectrum should transform simply and reasonably when the process is transformed linearly, and should lead to information about the important response statistics. Presented in this paper are some useful transform relationships for linear causal systems in terms of C. H. Page's time-varying spectra. Expressions suitable for direct analysis or numerical computation of the time-history of the response process and its bounds, the response power spectrum, the total energy of the system, and the upper bounds on the response shock spectra are given.