The current rise in popularity of ballisto-cardiography-related research has led to the development of new sensor concepts and recording methods. Measuring the ballistocardiogram using bed mounted pressure sensors opens up new possibilities for home monitoring applications. The signals measured with these sensors contain a mixture of cardiac and respiratory components, which can be used for detection of comorbidities of heart failure like apnea or arrhythmia. However, the separation of the cardiac and respiratory components has proven to be difficult, since there is significant overlap in the spectra of both components. In this paper, an algorithm for the separation task is presented, which can overcome the problem of overlapping spectra. Additionally, a model has been developed for the generation of artificial ballistocardiograms, which are used to analyze the separation performance. Furthermore, the algorithm is tested on preliminary data from a clinical study.