The variability of the heart rate (HRV) is widely studied as it contains information about the activity of the autonomic nervous system (ANS). However, HRV is influenced by breathing, independently of ANS activity. It is therefore important to include respiratory information in HRV analyses in order to correctly interpret the results. In this paper, we propose to record respiratory activity and use this information to separate the tachogram in two components: one which is related to breathing and one which contains all heart rate variations that are unrelated to respiration. Several algorithms to achieve this have been suggested in the literature, but no comparison between the methods has been performed yet. In this paper, we conduct two studies to evaluate the methods' performances to accurately decompose the tachogram in two components and to assess the robustness of the algorithms. The results show that orthogonal subspace projection and an ARMAX model yield the best performances over the two comparison studies. In addition, a real-life example of stress classification is presented to demonstrate that this approach to separate respiratory information in HRV studies can reveal changes in the heart rate variations that are otherwise masked by differing respiratory patterns.