Magnetic Resonance Fingerprinting (MRF) is an MR technique that generates parameter maps by matching pseudo randomly generated MR signals with a precalculated dictionary. In order to acquire the signals in a reasonable time, rapid imaging techniques with high undersampling factors are necessary. We show a detailed analysis of the artifacts originating from this and their impact on measured signals and subsequently on parameter maps. Additionally, an analytical approach of predicting undersampling artifacts is proposed. With the help of this approach, a more robust and time efficient sampling of signals in MRF can be designed.