For incoherent and coherent digital holography, the parallel phase-shifting technique has been used to reduce the number of exposures required for the phase-shifting technique which eliminates zero-order diffraction and conjugates image components. Although the parallel phase-shifting technique can decrease the hologram recording time, the image interpolations require additional calculation time. In this study, we propose a technique that reduces the calculation time for image interpolations; this technique is based on the convolution theorem. We experimentally verified the proposed technique and compared it with the conventional technique. The proposed technique is more effective for more precise interpolation algorithms because the calculation time does not depend on the size of interpolation kernels.