## 1 Introduction  
An increasing amount of economic and technological resources are being invested in accelerating the early detection of respiratory diseases (for example, pneumonia) as it is essential to providing effective medical treatment that minimizes risks to the health of the patient and optimizes healthcare costs at the same time. According to the World Health Organization (WHO), pneumonia is the leading cause of death in children, with one million deaths in children under 5 years of age in 2017, which is equivalent to 15% of all deaths in this population worldwide [1]. Although there are more sophisticated clinical tests (for example, blood tests and chest X-rays) to diagnose most lung diseases than the ausculation process [2], ausculation is the most widely used tool in health centers in low-income countries and even in most rural areas of high-income countries when a first respiratory system examination is performed mainly due to its low cost and non-invasiveness. However, auscultation depends largely on the acoustic training of each pulmonologist to recognize, through the stethoscope, the presence of abnormal sounds that are often associated with various respiratory pathologies, as occurs between crackles and specific lung diseases such as congestive heart failure and pneumonia [3; 4; 5]. In addition, it is important to note that crackles may not be heard by the doctor due to their short duration, low rate of occurrence, and often low amplitude, which makes them difficult to be detected by the human auditory system [6]. Respiratory sounds can be categorized into normal and abnormal sounds according to the COMPuterized Respiratory Sound Analysis (CORSA) guidelines [7]. Normal respiratory sounds (RSs) heard in healthy lungs are represented by a broadband spectrum locating most of the energy between 60-1000 Hz [8]. One of these abnormal or adventitious respiratory sounds are called crackles sounds (CSs), which are superimposed onto the RS, generated by unhealthy lungs as a consequence of pulmonary disorders. Crackles can be defined as discontinuous, short, explosive, and non-musical sounds with a spectral energy located between 100 Hz and 2000 Hz [9] as shown in Figure 1. Specifically, crackles can be classified as either coarse or fine. Coarse crackle sounds (CCs) are characterized by a temporal duration \(\leq\)20 ms and can be heard in the early inspiratory and the expiratory phases, showing a low pitch located around 350 Hz. One of the causes of these is the presence of air bubbles in large bronchi [10]. Fine crackle sounds (FCSs) are characterized by a temporal duration of \(\leq\)5 ms, active in the late inspiratory phase with a high pitch located around 650 Hz. The cause of FCSs is the abrupt opening of small airways [10]. In the literature [11; 12; 13], it is common characterize both CCSs and FCSs using temporal waveforms by means of two parameters: (i) \(t_{IDW}\) (initial deflection width), which indicates the temporal duration between the beginning of the crackle and the first deflection; and (ii) \(t_{2 CD}\) (two-cycle deflection), which represents the time duration from the beginning of the crackle to the time point where two cycles are completed. Specifically, (i) FCSs show on average \(t_{IDW}=0.5\) ms and \(t_{2 CD}=3.3\) ms whereas CCSs are represented on average by \(t_{IDW}=1.0\) ms and \(t_{2 CD}=5.1\) ms according to [PERSON] et al. [11]; (ii) FCSs show on average \(t_{IDW}=0.9\) ms and \(t_{2 CD}=6.0\) ms whereas CCSs are represented on average by \(t_{IDW}=1.25\) ms and \(t_{2 CD}=9.50\) ms according to [PERSON] et al. [12]; (iii) FCSs show on average \(t_{IDW}=0.7\) ms and \(t_{2 CD}=5\) ms whereas CCSs are represented on average by \(t_{IDW}=1.5\) ms and \(t_{2 CD}=10\) ms according to the American Thoracic Society (ATS) [13]. Figure 1: Magnitude spectrogram of a respiratory sound signal with a duration of ten seconds. The crackle sounds often tend to show vertical lines due to their short duration and explosive nature.