## 4 Practical Example of the Proposed Method  
The method proposed in this study was applied to the detection of noise-defects in an assembly line for ACs. The indoor AC unit is equipped with various types of fans to spread cold air in a room. However, if a problem occurs with constantly rotating fans or components around the fan, abnormal noise related to the rotation frequency of the fan is generated. The abnormal noise causes degradation of the product quality and consumer dissatisfaction. Therefore, companies that produce ACs have an inspection process to thoroughly sort out noise-defects before shipping out products. In this process, noise-defects had been detected using the senses of workers. Recently, an automatic system has been developed to detect noise-defects by analyzing the noise signal measured near a product and has been installed in factories. However, in the site where noise is measured, there are various noises caused by random sources in other assembly processes, which make it difficult to detect defects effectively. Although an additional soundproof booth is installed to block out unpredictable noises from other processes, it not only can not completely block out the noises, but also increases the burden for cost and space. In particular, the impulsive noise caused by a conveyor belt moving products makes it more difficult to detect noise-defects. Figure 12a shows the STFT of the acoustic signal of a normal AC measured for 5 s inside a soundproof booth where the product can enter and exit by a conveyor belt. The sounds from the back of ACs were measured for 5 s by fixed microphones while the ACs were moved at equal distance by the conveyor belt. The situation being measured was not controlled for testing, it was actually in production. In this figure, the impulsive noise seen at around 3 s (big white line circle) was investigated as noise caused by other technical  
Figure 11: The result of the proposed method to the signal models. The difference between the magnitude at rotational frequency and the baseline lower frequencies in short time envelope spectrum: (**a**) case without impulsive noises; (**b**) case in the presence of impulsive noise at 0.1 s; (**c**) case in the presence of four impulsive noises at 0.1, 0.4, 0.5, and 0.8 s.  
processes. It was confirmed that the noise observed between 2 and 3 kHz and around 1 s (small white line circle) was introduced from the outside. Figure 12b shows the STFT of the acoustic signal of the AC investigated as a noise-defect caused by foreign substances hitting the blower fan. As the blower fan rotates, periodic noise is generated whenever it hits foreign substances. In order to automatically detect this noise-defect, the time-frequency envelope analysis method proposed in this study was applied. A bandpass filter with cut-off frequencies of 3 and 6 kHz was applied to extract the signature of abnormal noises in conventional envelope spectrum. The bandwidth and center frequency of the filter were selected as the band representing the difference between normal and abnormal in frequency spectrum investigated in anechoic chamber conditions. At this time, frequencies of 2 to 3 kHz were not included in the band to exclude a beep sound that is not related to the noise-defect. Figure 13 shows the band-pass filtered time signal. Figure 13a,b shows the acoustic signals of the normal AC and the noise-defective AC, respectively. In the upper left of Figure 13a, the section between 0.5 and 1.5 s is enlarged and shown in the same scale as Figure 13b. Periodic impact signal, a feature of defective signal, is not observed. In Figure 13a, the impulsive noise is clearly visible at around 3 s, and no distinctive features appear in other time zones. On the other hand, in Figure 13b, the abnormal noise has the same period as the fan's rotation speed and occurs in the form of impacts.