## 1 Introduction
[21] conducted envelope analysis using long pass liftered cepstrum and wavelet denoising as noise reduction methods. Cepstrum is known as inverse Fourier transform of the logarithmic spectrum of the signal. Numerous studies on noise-removal methods for envelope analysis have focused on Gaussian noise or deterministic parts of gears [22; 23; 24]. In this paper, impulsive noise means short-time noise independent of the measurement signal, such as external noise that may occur when a door is slammed, external knocks on the bearing housing, and electromagnetic interference. There can be many unpredictable noises on the factory floor and industrial application, such as noises generated by other technical processes around the inspection sites or by the activities of workers [18; 25; 26]. To address this issue that degrades the performance of the CS-approach-based method in impulsive noise environment, various methods have been proposed, such as cyclic correntropy [13; 27; 28], gini-index guided bearing fault diagnosis to replace kurtosis [18], and infogram using both periodicity and impulsiveness of fault signature [14]. Cyclic correntropy shows good performance of the fault diagnosis even in the presence of impulsive noise, but there is concern about computation time. [PERSON] et al. [17] proposed an optimized spectral kurtosis method that can be applied to signals with poor kurtogram and prottrugram performance due to electromagnetic interference noise. Indeed, on the factory floor, efforts have been made to improve the detection rate of noise-defects by making soundproof rooms that block various noise, including impulsive noise [5; 29; 30; 31]. However, it is difficult to completely block impulsive noise because it has high energy in a wide frequency range within a short time. In the previous studies for condition monitoring or defect detection in impulsive noise environment, deep perceptions of the mathematical approaches are required for practical application. We propose a simple approach based on time-frequency analysis for defect detection or condition monitoring in the presence of impulsive background noise. Because time-frequency analysis combines both information in the time and the frequency domain, it is thus an effective approach for non-stationary signal analysis in machine fault diagnosis [32; 33]. Many methods based on time-frequency analysis have been proposed for effective condition monitoring or defect detection [4; 33; 34; 35; 36]. To mitigate the effects of impulsive noises independent of the fault signal of a rotating machinery, envelope analysis using a time window was first performed and the frequency response characteristics of a single short time rectangular wave was used. The proposed method was validated using synthetic signals modeled as a CS process and real data measured in an air-conditioner (AC) production line. The contribution of the proposed method is simple, easy to apply, and can alleviate the strict constraints of the environment for fault diagnosis. This method also helps diagnose faults using microphones, which are non-invasive sensors but are sensitive to background noise [5]. In the future, approaches of big data [8; 37; 38] and deep learning [39; 40] will be needed to develop failure prediction and prognostic health management (PHM) technology. The rest of this paper is organized as follows. Chapter 2 describes the modeling of a CS signal representing the characteristics of a rotating machinery. Then, through simulation of the modeled synthetic signal, it shows the performance degradation of envelope analysis caused by contamination of impulsive background noises. In chapter 3, it is verified that defect detection through envelope analysis is improved by applying the proposed method to the signal model. In chapter 4, the real case is presented to verify the effectiveness of the proposed method by using normal and defective signals measured on an assembly line for ACs with fans as rotating machine parts.