## 3 Methodology  
This work proposes to study the FHR signal characteristics with a focus on the dynamics resulting from ANS modulation. The main idea is to extract signal features from the entire signal, during decelerations and resting periods, thereby investigating whether by analyzing such FHR signal segments separately, the CTG classification can improve compared with the traditional analysis based on the entire signal. After a perceived oxygen insufficiency, as a first fetal response, the sympathetic nerves may act as a compensatory mechanism to improve the fetal heart-pumping activity, whereas the parasympathetic ANS activity may decrease [24; 44]. In contrast, after the perceived threat (oxygen insufficiency) has been attenuated, the parasympathetic ANS may be activated, and the sympathetic activity decreases. That interaction is a normal phenomenon; however, in some cases, these physiological mechanisms may be weakened, leading to fetal distress. Besides, in fetuses, the sympathetic ANS system predominates, because it develops earlier than the parasympathetic ANS system, which becomes more developed with advancing maturity [29]. Therefore, the main goal of our work, as several related approaches proposed in the literature [26; 39; 45], was to extract information from an FHR signal related to the sympathetic ANS activity in order to estimate a fetus's state of health. As explained above, the FHR data involves highly complex characteristics mainly associated with their nonlinear and non-stationary behavior as a result of the ANS activity [11]. Therefore,it is reasonable to think that if such characteristics are not previously demodulated or decomposed, the extraction of the information of interest could be a difficult task. On the other hand, conventional signal processing methods can no longer be used for the analysis of those characteristics, because they are not appropriate to describe this time-variant physiological phenomenon. In this context, we propose an approach that combines two signal processing techniques: CEEMDAN [46] and TV-AR modeling [47] for the analysis in the time- and spectral-domain, respectively. On the one hand, CEEMDAN is an adaptive technique that allows decomposing non-stationary and nonlinear time series into IMFs, which are computed by the direct extraction of the energy associated with the signal oscillations. The CEEMDAN decomposition operation is based on similar principles of signal demodulation in amplitude; therefore, we postulate that this method can be useful for extracting the information of interest involved in the FHR dynamics as a result of the ANS modulation. Consequently, the main advantage of CEEMDAN is its dependency on the data-driven mechanism, which does not require a priori known bases as in the case of other traditional techniques such as wavelet and FFT-based decomposition [48; 49; 50; 51]. On the other hand, in order to examine the frequency information involved in the IMFs, we employ TV-AR spectral-based analysis. It is a technique for time series analysis based on a mathematical model fitted to a sampled signal. Therefore, it has several advantages for the analysis of the FHR signal because this model provides a signal description that makes it easier to analyze by a few model parameters. Besides, it allows the extraction of quantitative time-dependent spectral parameters, which are better suited for quantitative analysis [32]. In the spectral-domain, the information of interest involved in the IMFs is represented by the power spectral density peaks, which represents the contributions of their time-variant frequency components. Additionally, considering that the sampling frequency of the FHR signals we studied was the only 4 Hz, the AR modeling was appropriate for the IMF, spectral-based analysis. The AR modeling method effectively describes the peaks of a narrow-band power spectrum [52], and it requires only a fraction of the signal samples that are needed by standard methods, such as the FFT, in order to obtain the same spectral resolution.