The heart rate in humans is regulated by the autonomic nervous system, which modulates the frequency of heart contractions, resulting in heart rate variability (HRV). Therefore, to assess the activity of the autonomic nervous system, which contains important information for medical diagnostics, methods based on the analysis of interbeat interval variability are often used. This approach does not require the use of invasive methods for measuring the signals of the autonomic nervous system, but its accuracy is an open question. Using mathematical modeling, we investigate the possibility of extracting the signal of frequency modulation of the heartbeats from the electrocardiogram (ECG) signal and conduct a detailed comparison of the extracted signal with the real modulating signal. Since the quality of extraction of the signal of frequency modulation from the ECG depends on the method of demodulation, we compare two different approaches. One is based on the detection of the main oscillation rhythm and its bandpass filtering, and the other on the heterodyning technique. It is shown that low-frequency (LF) and high-frequency (HF) oscillations in HRV associated, respectively, with sympathetic and parasympathetic modulation by the autonomic nervous system, in the general case, significantly differ from the signals of frequency modulation of the heart rate in shape, but have close similarity with them in the frequency domain. We find that in model systems, the similarity of the LF component of HRV with sympathetic modulation of the heart rate is higher than the similarity of the HF component of HRV with parasympathetic modulation.