## 1 Introduction  
Cardiovascular diseases are one of the leading causes of death in the world. According to recent reports from the World Health Organization and the American Heart Association, more than 17 million people die each year from these diseases. Most of these deaths (about 80%) occur in low- and middle-income countries [1, 2]. Tobacco use, unhealthy eating, and lack of physical activity are the main causes of heart disease [1]. Currently, there are sophisticated equipment and tests for diagnosing heart disease, such as: electrocardiogram, holter monitoring, echocardiogram, stress test, cardiac catheterization, computed tomography scan, and magnetic resonance imaging [3]. However, most of this equipment is very expensive, and must be used by specialized technicians and medical doctors, which limits its availability in rural and urban areas that do not have the necessary financial resources [4]. Therefore, even today, it is common in such scenarios for non-specialized medical personnel to rely on basic auscultation with an stethoscope as a primary screening tool for the detection of many cardiac abnormalities and heart diseases [5]. However, to be effective, this method requires a sufficiently trained ear to identify cardiac conditions. Unfortunately, the literature suggests that in recent years such auscultation training has been in decline [6; 7; 8]. This situation has motivated the development of computer classification models to support the identification of normal and abnormal heart sounds by non-specialized health professionals. To date, many investigations related to the analysis and synthesis of heart sounds (HSs) have been published, obtaining good results especially in the classification of normal and abnormal heart sounds [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. Heart sounds are closely related to both, the vibration of the entire myocardial structure and the vibration of the heart valves during closure and opening. A recording of heart sounds is composed of series of cardiac cycles. A normal cardiac cycle, as shown in Figure 1, is composed by the S1 sound (generated by the closing of the atrioventricular valve), the S2 sound (generated by the closing of the semilunar valve), the systole (range between S1 and S2), and the diastole (range included between S2 and S1 of the next cycle) [26]. Abnormalities are represented by murmurs that usually occur in the systolic or diastolic interval [27]. Health professionals use different attributes of heart murmurs for their classification, the most common are: timing, cadence, duration, pitch, and shape of the murmur [28; 29]. Therefore the examiner must have an ear sufficiently trained to identify each of these attributes. Despite the amount of work related to the classification of heart sounds, it is still difficult to statistically evaluate the robustness of these algorithms, since the number of samples used in training is not sufficient to guarantee a generalized model. Similarly, there have been no significant advances in the classification of specific types of heart murmurs, due to the limited availability of corresponding labels in current public databases [30; 31]. In this sense, having a model for the generation of synthetic sounds, capable of outputting varied synthetic heart sounds indistinguishable from natural ones by medical personnel, could be used to augment existing databases for training robust machine learning models. However, heart sound signals are highly non-stationary, and their level of complexity makes obtaining good generative models very challenging. In the literature, there are several publications related to the generation of synthetic heart sounds [16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. All these works are based on mathematical models to generate the S1 and S2 sections of a cardiac cycle. On the other hand, the systolic and diastolic intervals of the cardiac cycle are not adequately modeled, and as a result, do not present the variability recorded in natural normal heart sounds.