Computer-generated Fourier holograms (CGH's) can be used to carry information in data storage, display, and incoherent image processing situations. The reconstructed intensity I(x,y) represents the data in case of data storage and display and the desired impulse response function in case of incoherent image processing. The Fourier transformation (FT) fr(v,p) of a complex amplitude u(x,y) = VI(x,y) exp(i0(x,y)) is the basic distribution needed to produce CGH's which reconstruct the intensity I(x,y). The phase 0(x,y) of the complex amplitude u(x,y) does not affect the intensity I(x,y) and in this sense it is a free parameter. This freedom can be used to increase the diffraction efficiency and the redundancy of the CGH and to reduce quantization errors introduced by the hologram generation process.A powerful method to achieve these aims is " pp smooth the power spectrum of u(x,y) by superimposing a suitable phase distribution onto 1u(x,y)1.However, it is not possible to use any arbitrary phase distribution. The resulting complex amplitude has to be bandlimited because the size of the CGH is finite. Disregard of this requirement will lead to defects in the reconstructed intensity, e.g., the introduction of a random phase (diffuser) in computer and optical holography leads to speckles in the reconstruction. We want to use an iterative FT algorithm') to obtain a bandlimited complex amplitude u(x,y) with a smooth power spectrum. Such a complex amplitude is the basis for elimination of speckles in the reconstructed image.