Evolutionary spectra, which capture the frequency profile change in time domain, is the key quantity in vibrations. An approach for estimating the evolutionary power and cross spectrum of nonstationary stochastic processes is developed through the determination of the total energy of lightly damped linear systems. In this regard, a novel approach is discussed for appropriately smoothing the total energy of a linear single degree of freedom (SDOF) system, based on the use of Savitzky-Golay moving average filter. Further, a novel approximated energy function is proposed to fit the numerical total energy of the SDOF system. Then, the evolutionary power and cross spectrum can be generated by the approximated energy function. In this thesis, several numerical applications have been used to test the accuracy and reliability of the proposed energy function. In this regard, uni- and multi-variate nonstationary stochastic processes are simulated through the autoregressive (AR) algorithm and spectral representation method. Then, the evolutionary power and cross spectrum of simulated time series are estimated and compared to the target evolutionary power and cross spectrum to assess the reliability of the proposed method. Furthermore, real earthquake data are used to estimate the corresponding evolutionary spectra by the proposed approach, and accuracy of the results is proved by comparing with the evolutionary spectra obtained by generalized harmonic wavelets (GHWs) transform.