A coherent optical imaging system consisting of recording a digital hologram by a CCD array and numerical reconstruction of the complex wave field in a computer is subjected to a frequency analysis. This analysis recognizes Fresnel and lensless Fourier transform holography; collimated and divergent reference waves; as well as the real image, the virtual image, and the dc term. The influences of finite sampling and the fill factor of the CCD pixels are examined. The impulse response of the system is a shifted Fraunhofer diffraction pattern of the aperture defined by the CCD. A fill factor below unity leads to a contrast decrease, which is quantitatively described in the modulation transfer function.