The present manuscript is dedicated to the development of a holographic data storage (HDS) system based on computer generated Fourier holograms (CGFH). The application of advanced modulation methods such as phase modulation and spatial quadrature amplitude modulation to represent digital data massives as complexly modulated two-dimensional data pages allows one to increase the information capacity of the HDS system. The application of CGFH for storing and reconstructing such data pages is discussed in this article. Particularly, the efficiency of implementation of different light modulation methods that can be used for CGFH transparency function physical realization, such as purely-amplitude, purely phase and combined amplitude and phase, are investigated by means of numeric simulations.