## 4 Experiments and Results
### Results Using Mel-Cepstral Distortion (MCD)  
Mel-cepstral distortion (MCD) is a metric widely used to objectively evaluate audio quality [46], and its calculation is based on Mel-frequency cepstral coefficients (MFCC). This method has been widely used in the evaluation of voice signals, since many automatic voice recognition models use feature vectors based on MFCC coefficients [46]. The parameters used for MFCC extraction are the following: the length of the analysis window (frame) in seconds is 0.03 s, the step between successive windows in second is 0.015 s, the number of cepstra to return in each windows (frame) is 14, the number of filters in the filterbank is 22, the FFT size is 4000, the lowest band edge of mel filters is 0, the highest band edge of mel filters is 0.5, and no window function is applied to the analysis window of each frame. Basically, MCD is a measure of the difference between two MFCC sequences. In [PERSON] and [PERSON] [47], different ways of calculating this distortion are presented. In Equation (3), the formula used in [46] is defined, where \(C_{MFCC}\) and \(\hat{C_{MFCC}}\) are the MFCC vectors of a frame of the original and study signal, respectively, and \(L\) represents the number of coefficients in that frame. \(MCD_{FRAME}\) represents the MCD result obtained in a frame. \[MCD_{FRAME}=\sum_{l=1}^{L}\left(C_{MFCC}[l]-\hat{C_{MFCC}}[l]\right)^{2} \tag{3}\]  
In this work, it was decided to use this objective measurement method to evaluate the similarity between natural and synthetic heart signals, taking into account that heart sounds are audio signals \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Index (i)** & **S1 (-)** & **S1 (+)** & **S2 (-)** & **S2 (+)** \\ \hline \(a_{i}\) & 0.4250 & 0.6875 & 0.5575 & 0.4775 \\ \hline \(\mu_{i}\) (radians) & \(\pi/12\) & \(3\pi/19\) & \(3\pi/4\) & \(7\pi/9\) \\ \hline \(\sigma_{i}\) & 0.1090 & 0.0816 & 0.0723 & 0.1060 \\ \hline \(f_{i}\) (Hz) & 10.484 & 11.874 & 11.316 & 10.882 \\ \hline \(\varphi_{i}\) (radians) & \(3\pi/4\) & \(9\pi/11\) & \(7\pi/8\) & \(3\pi/4\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters used in [21] to generate normal heart sounds. Figure 9: (**A**) Synthetic heart sound generated by the model [21]: (**B**) natural signal of the heart sound. that are typically evaluated using human hearing, and the MFCC coefficients have already been used in the analysis of heart sound signals [9; 10; 11; 12]. A set of 400 natural normal heart sounds taken from the Physionet [30] and Pascal [31] databases were used. Each signal was cut to a single cardiac cycle, with a normalized duration of 1 s, applying a resampling on the signal. Signals were also normalized in amplitude, and those signals with a similar heart rate were chosen. Those natural signals are compared to a total of 50 synthetic heart sounds generated using the proposed method, and 50 synthetic signals were generated using the model [21]. In the case of the model [21], the \(\alpha_{i}\) parameters were obtained with random variables in the range of 0.3 to 0.7, in order to generate different wave signals. The other parameters were established as shown in Table 3. Additionally, the synthetic signal was mixed with a white Gaussian noise, as indicated in the article [21]. These synthetic signals have a sampling rate of 2 KHz, a duration of 1 s, and are amplitude-normalized. All signals (natural and synthetic) have a similar heart rate--that is, the size of the systolic and diastolic interval is similar in all the signals. The first evaluation step was to calculate the MCD between the natural signals--that is, the MCD between each natural signal and the remaining natural samples. A total of 399 MCD values were computed and then averaged. This same procedure was applied with the synthetic signals, i.e., computing the MCD between each synthetic signal and each natural signal, obtaining 400 MCD values that were then averaged. Figure 10 shows a schematic of the procedure to compute the MCD.