## 1 Introduction  
Within the fields of medicine and psychophysiology, spectral analysis of heart rate variability (HRV), and particularly high frequency HRV (HF-HRV), is increasingly used as a proxy of cardiac parasympathetic nervous system (PNS) regulation. The HF-HRV around 0.25 Hz mirrors respiratory fluctuation, i.e., respiratory sinus arrhythmia (RSA) [1]. High HF-HRV is suggested to be associated with fast cardiac regulation that promotes attention and engagement to environmental demands [2; 3; 4]. Reduced HF-HRV is related to, for example, attention deficits, depression, various anxiety disorders, long-term work related stress or burnout, and cardiovascular diseases [5; 6; 7]. To optimize methods that reliably quantify HF-HRV is consequently important, not the least for being able to detect cardiovascular deviations at an early stage that in the long run will lead to disease. In general, 2-5 min of electrocardiography (ECG) is used to estimate the HF-HRV power in a predefined frequency range, i.e., 0.12-0.40 Hz, corresponding to the range within which we normally breathe [1]. However, such a rather wide frequency band does also include power from frequencies that are not RSA-related, which most likely is highly irrelevant information regarding RSA, as discussed in [8; 9; 10]. This procedure will also give an incorrect power estimate when the breathing frequency is no longer within or close to the pre-defined frequency range, 0.12-0.40 Hz, e.g., in connection with exercise and stress testing [11; 12; 13]. Therefore, it is of great importance to obtain the instantaneous respiratory frequency (IRF) estimate and use it as a reference to estimate the instantaneous power of the heart rate (HR) signal. Consequently, only information that is of interest, i.e., HR variations due to respiration, without irrelevant signal information of unknown origin, is quantified. In prior studies [8; 9], we have examined if a narrowed HF-HRV band around the IRF would better capture respiratory related HR variation than the traditional 0.12-0.40 Hz band. The instantaneous HF-HRV band was then defined as \(\pm\)0.05 Hz around the IRF. To evaluate the two HF-HRV estimates, we calculated the correlation between IRF and HF-HRV power, which are negatively correlated to each other [14; 15; 16]. The results showed that the negative correlation between IRF and HF-HRV power was clearly more pronounced using the narrowed frequency band compared to the traditional one, suggesting that the narrowed HR-HRV band represents a more robust HF estimate. Other studies have found corresponding results, showing that power estimates of HF-HRV band based on the respiratory center frequency, as compared to a the traditional static HF-band, seem to be more reliable [12; 13]. A direct measure of the respiration data, e.g., using a strain gauge over the chest, gives a mono-component signal without any significant amplitude variation. An estimate of the IRF from this signal is therefore less error prone. Different time-based approaches to estimate the IRF exist, especially for analysis of respiration data for rest and sleep stages, e.g., [17; 18]. For non-stationary IRF, estimation related to exercise and stress tests and spectrogram based methods are applied [11; 19]. Usually, the extraction of IRF from the respiratory data has been shown to be reliable in these cases. It is also worth noting that, concerning instantaneous frequency estimation of a non-linear mono-component signal, the spectrogram is actually superior to the pseudo-Wigner-Ville distribution [20], if an appropriate window length is applied. Previous studies have shown that multi-component HR signals also have non-stationary characteristics [11; 19; 21]. Such signals are usually analyzed in the joint time-frequency domain (TFD) because the spectral contents of these signals change with time [22]. The spectrogram is computationally efficient and produces a positive TFD related to signal power.