## 1 Introduction  
Prognostics and Health Management (PHM), which enables life extension while preventing unexpected failures in various engineering systems, have received great attention over the last decades for more efficient operation and maintenance. Generally, there are three main steps in the PHM development: (1) signal processing, (2) diagnosis, and (3) prognosis. Signal processing is the step in which the valuable information called features are extracted from noisy sensor signals such as vibrations or acoustic emissions. Diagnosis focuses on detecting the faults, isolating their locations, and identifying their severity based on the extracted features. Lastly, the prognosis is to predict the Remaining Useful Life (RUL) based on the accumulated diagnostic information, which indicates how long it will take until the system's health reaches the failure threshold. Though the most important step is the prognosis, its performance is of no doubt dependent on the quality of prior steps: the signal processing and the diagnosis. To date, the PHM has mainly focused on the vibration signal-based techniques for rotating mechanical components such as gears [1,2] and bearings [3, 4, 5, 6, 7], since they usually lead to the critical failures [1,8]. Among them, the rolling element bearings, which support the shaft during the rotation, have been of greatest importance in view of its widespread use and often cause of another failures. For example, the bearings are known to cause around 70% of gearboxes and 21-70% of generator failures in the wind turbine industries [9]. To prevent such failures, early fault detection and diagnosis of the bearings is important. A great deal of research has been conducted on this topic. Many review papers are available, addressing the state-of-the-art algorithms from various perspectives. Only a few are given here; among others, [PERSON] et al. reviewed several signal processing techniques for the rolling element bearing fault diagnosis [10]. [PERSON] et al. have reviewed fault severity assessment methods [11]. [PERSON] et al. made review on artificial intelligence-based approaches including shallow and deep learning [12]. Reviews are available, too, on the bearings for specific applications; [PERSON] et al. presented feature extraction methods for the low-speed slew bearing [13]. [PERSON] et al. have reviewed condition monitoring methods for bearings in the wind turbine [9]. As such, a great number of new algorithms have been introduced and reviewed over the last decades. Despite the importance, however, no studies have dealt with the tutorial aspects except the one by [PERSON] and [PERSON], which have introduced a number of techniques covering the essential as well as advanced algorithms in the context of diagnostic procedure [14]. The paper was highly informative and enlightening in several aspects, but it was in some sense close to a collection of their recent achievements in a single article, and hence was less instructive in view of the self-explanatory aspects of the tutorial. In real practice, there are many instances that engineers without enough knowledge in this field fail to solve their problems due primarily to the lack of detailed understanding of the algorithms and of how to implement them. Motivated by this, a tutorial is presented in this paper to conduct the fault diagnosis of rolling element bearing, with the purpose to help the beginners learn by themselves the basic concepts along with implementing the algorithms with minimum resort to the external resources. Among the techniques currently available for the bearing diagnosis, envelope analysis is the most common and relatively well established, which enables to detect the fault with location by matching the frequency spectrum of the envelope to the fault frequencies. By the way, the bearing signal is usually masked by the resonant noise and those coming from other components (e.g., gears and engines), which should be filtered out as a first step.