Abstract: Certain types of finite-difference approximations for time derivatives have traditionally been used for integrating hydrodynamical equations because of their know damping properties. For meteorological models, we have a multiple scale presence of high-frequency gravity waves and slow Rossby waves, which difficulties the successfull development of numerical forecasting. Tha Laplace transform technique was suggested as a method for initialization and integration, which consists in the projection of the model equations in the complex plane where a contour, approximated by an inscribed polygon, specify a critic frequence. A backward projection to the real physical space gives an initial state with efficient attenuated high frequencies. This method was also used in the time-integration of a baroclinic model. The permanent filter properties has the benefit of allowing a time step which is sensible larger than the classical time-differencing schemes. In this work, we apply the impulse invariance transformation to the operational equation of a given equation and sample its solution at M points in a convenient way. We then reconstruct a filtered initial data by iterating it with the inverse Fourier discrete transform. It is made, in such a way that the r-th iterate of the solution at the origen is just the Fourier matrix times a filter G and a transform of the linear part times earlier iterate minus the initial non-linear contribution. The filter G eliminates frequencies outside the bands $[0, \nu ]$, $[M - \nu, M - 1]$ with $\nu$ equal M times desired cutoff frequency $f_s$. This filter is sharper than the one used with the Laplace transform and there is no phase alteration. By considering the first harmonic, we could easily choose a cutoff frequency of the solution spectrum in such a way that the transfer function of the linear part of the system vanishes for high frequencies. Then to approximate the solution by a linear combination of sino functions. We expect that this method confirms numerical experiments which are on the way.