Three types of loads are typical in vibration fatigue: random, harmonic and impact. In an application, any combination of these loads is possible. In vibration fatigue the random loads can be investigated by using the frequency-response function of the structure. While the theoretical relationship between the frequency-response function and the impact-response function is clear (they form the Fourier pair), the time/frequency relationship of vibration-fatigue damage has not yet been investigated in detail. The focus of this research is a theoretical study of the time- and frequency-domain damage of a single-degree-of-freedom dynamic system under well-separated half-sine impulse excitation. The introduced theoretical relationship between the time- and frequency-domain (Narrow-band and Tovo-Benasciutti method) damage showed that the significantly different results are related to the underlying dynamic properties (e.g., natural frequency and damping) of a flexible system. Based on the introduced relationship, the frequency-domain damage estimation is corrected for a reliable damage estimation. In addition, an experimental test case is presented. The introduced theoretical relationship opens up new possibilities to investigate the impact excitation in the frequency domain and provides the necessary theoretical background for applications when the impacts are not well separated and start to overlap, resulting in the broadband excitation observed in clearance contacts.