The main objective of the GOLF Experiment (Global Oscillations at Low Frequencies) on-board the SOHO (Solar and Heliospheric Observatory) space mission is the quantitative knowledge of the internal structure of the Sun by measuring the spectrum of its global oscillations in a wide frequency range (30 nHz to 6 mHz). There is special interest in detecting the low l p- and g-modes (low frequency modes) which penetrate deeply down into the solar core. The instrument chosen is an improved disk-integrated sunlight resonant scattering spectrophotometer. It obtains the line of sight velocity of the integrated visible solar surface by measuring the Doppler shift of the sodium doublet. Mainly, two innovations have been incorporated to standard earth-based similar apparatus (those from the networks IRIS and BISON). First, GOLF samples each line of the sodium doublet in principle at four points on its wings, using an extra small modulated magnetic field. This new information enables an instantaneous calibration of the measured signal and also opens the possibility to correct from the background solar velocity noise. Second, the use of an extra fixed quarter wave plate, placed at the entrance of the instrument, enables a selection of the circularly polarized solar light. Therefore, the disk averaged solar line-of-sight component of the magnetic field can also be obtained. This is considered as a secondary objective of the mission. In order to study the new information available due to these improvements in the apparatus, the necessity of fully understanding it and the need to write the appropriate software to analyze the data, a complete numerical simulation of the experiment has been built. Running the simulation has yielded two series of 12 months long each, one corresponding to a year of maximum solar activity and the other to a year of minimum solar activity. In this paper the numerical simulation of the GOLF experiment is presented, its sensitivity and instrumental response calculated and a power spectra of this two series have been obtained to show its performance against the observations. It is shown that the numerical simulation explains the observed spectra of the solar background velocity signal and the oscillations to a high degree of accuracy.