Analytical expressions for a) the frequency average of transfer functions, b) the frequency variance of transfer functions, and consequently, c) the frequency average of the energy of linear dynamic systems are available from the author’s previous work [1].  Since these expressions are valid and can be evaluated at any frequency, independently of the system complexity and modal density, they provide a natural framework in which to study the transition from low- to high-frequency ranges.  In principle, the analytical expressions would require the knowledge of the modal characteristics of the dynamic system of interest.  Here, the fact that modal information is not needed to evaluate the frequency average of transfer functions is presented.  Rather, the average can be evaluated up to desired precision by using an analytical Krylov model reduction approach.  The efficiency of this approach is demonstrated on systems of different dimensions and modal densities.   It is further demonstrated that system characteristics that are important at different frequency ranges can be integrated into a single reduced model and that low- to high-frequency ranges analysis can be run with a single model.