A moving average (MA) is a commonly used noise reduction method in signal processing. Several studies on wheeze auscultation have used MA analysis for preprocessing. The present study compared the performance of MA analysis with that of differential operation (DO) by observing the produced spectrograms. These signal preprocessing methods are not only applicable to wheeze signals but also to signals produced by systems such as machines, cars, and flows. Accordingly, this comparison is relevant in various fields. The results revealed that DO increased the signal power intensity of episodes in the spectrograms by more than 10 dB in terms of the signal-to-noise ratio (SNR). A mathematical analysis of relevant equations demonstrated that DO could identify high-frequency episodes in an input signal. Compared with a two-dimensional Laplacian operation, the DO method is easier to implement and could be used in other studies on acoustic signal processing. DO achieved high performance not only in denoising but also in enhancing wheeze signal features. The spectrograms revealed episodes at the fourth or even fifth harmonics; thus, DO can identify high-frequency episodes. In conclusion, MA reduces noise and DO enhances episodes in the high-frequency range; combining these methods enables efficient signal preprocessing for spectrograms.

The possibility of a normal distribution indicates that few particles are in the same phase during a breath and their reflections can be observed on the chest wall, then a few explosive waves with relatively large power occurr occasionally. Therefore, the one-cycle sine wave which is simulated as a single burst of the explosive effect phenomenon penetrates through the chest wall and was analysed to explore the reason of the crackle sounds. The results explain the differences between the definitions of crackle proposed by Sovijärvi et al. (2000a). The crackles in the lungs were synthesised by a computer simulation. When the coarse crackles occur, the results indicate that higher burst frequency carriers (greater than 100 Hz) directly penetrate the bandpass filter to simulate the chest wall. The simulated coarse crackle sounds were low pitched, with a high amplitude and long duration. The total duration was greater than 10 ms. However, for a lower frequency carrier (approximately 50 Hz), the fundamental frequency component was filtered out. Therefore, the second harmonic component of the lower frequency carrier, i.e., the fine crackle, penetrated the chest wall. Consequently, it is very possible that the normal lung sounds may contain many crackle-shaped waves with very small amplitudes because of the filtering effects of the chest wall, environment noises, electric devices, stethoscopes, and human ears, the small crackles disappear in the auscultations. In addition, our study pointed out that some unknown crackles of the very low frequency under the bandwidth of the human ears cannot penetrate the airways and be detected by medical doctors. Therefore, it might be necessary to focus advanced electronic instrumentation on them in order to analyse their possible characteristics for diagnosis and treatment of the respiration system.