In recent years the field of digital holography became an attractive research area following the developments of CCD-arrays and an ever increasing computational power of computers. Here we investigate digital holography reconstruction methods and compare them for the accuracy and the computational speed. In addition, possible discrepancies in the calculation of the diffraction integral via fourier transform is clarified and it is compared to convolution methods. The proper evaluation of discrete Fresnel diffraction equation is demonstrated by creating artificial holograms and numerically reconstructing them. Simulation results and experimental work is presented.