Digital holography is widely used in many fields for imaging, display, and metrology by exploiting its capability to furnish quantitative phase contrast maps. The entire processing pipeline that permits achievement of phase contrast images can be obtained by a cascade of numerical processing, such as zero-order and twin-image suppression, automatic refocusing, phase extraction by aberration compensation, and, if necessary, phase unwrapping. In this paper, we propose a new method, to the best of our knowledge, based on singular value decomposition filtering, to suppress zero-order and twin images in off-axis configuration, thus, automatically selecting the desired real diffraction order. We demonstrate the proposed approach in the case of lack of knowledge about the reference beam's frequency and curvature, which typically occurs in portable off-axis holographic microscope systems for lab-on-a-chip applications. We validate the proposed strategy by a comparison with common Fourier spatial filtering in the case of different experimental conditions and for several biological samples.