In Chapter 2, the theoretical background for obtaining a nonstationary stochastic response of a single-degree-of-freedom (SDOF) system subjected to a random vibration process in the wavelet domain is clearly shown. The formulation to obtain peak stochastic responses of a system is elaborated in the same chapter. Users should keep in mind that to study the response of a system subjected to nonstationary ground motions, it is necessary to characterize the seismic process through statistical functionals of wavelet coefficients. The ground motion characterization has been attempted before by researchers using different approaches like spectrum-compatible wavelet functionals for the input Fourier spectrum and input response spectrum. In any ground motion, peak horizontal ground acceleration is important, as it is directly related to the damage potential. However, the duration of strong shaking, the energy and frequency contents, peak ground velocities and displacements, etc. also affect the extent of damage in structures. The frequency content of earthquake ground motion is generally characterized by the shape of the acceleration response spectrum. The energy content in the spectrum is directly proportional to the square of the acceleration. In this chapter, we will see how the wavelet coefficients generated from a single ensemble are used to characterize ground motions, and how this characterization is subsequently used to obtain the pseudospectral acceleration (PSA) response spectrum of a SDOF system.