In 2008, S. Rezaeian and A. Der Kiureghian introduced a new fully nonstationary stochastic model for strong earthquake ground motions. The model employs a parameterized stochastic model, which is based on a modulated Gaussian white noise. In 2010, the same authors used this work as a base for developing a new method for generating a family of synthetic ground motion time-histories for specified earthquake and site characteristics. The model is both used in seismic analysis in substitution or conjunction with recorded ground motions and in seismic reliability assessment via simulation methods or TELM analysis (K. Fujimura and Der Kiureghian, 2007). The method was developed in the time domain, with the discretization of the time axis in a set of equally spaced time points. A set of Gaussian random variables, representing the random pulses at the discrete points in time, is used to describe the white noise. This discretization usually leads to a large number of random variables. While in the simulation methods this number is not playing a significant role, in TELM analysis this number is crucial in determining the computational cost. If the frequency domain discretization is employed, Garrè and Der Kiureghian (2010) have shown that the number of random variables can possibly be significantly reduced. In this talk we present a variation of the original model, where the frequency domain discretization is employed in substitution of the time domain discretization. We present the advantage and the disadvantage of one method over the other. Finally, we examine with an unusual “acoustic performance” the pitfalls that users should be aware of in using these models.