## 1 Introduction  
Gearboxes play an important role in numerous industrial machines, vehicles, and wind turbines [1, 2, 3]. Due to the operation of gearboxes in harsh conditions, gear defects are found to be the most common defects in gearboxes [4]. A fault in the gearbox can result in catastrophic failures, economic losses, and danger to the operating staff. For this reason, early fault detection of the gearbox is of primary importance. The condition-based monitoring approach suggests maintenance action based on the data collected from the gearbox. This strategy allows the gearbox to function for a long time with minimal maintenance costs [5, 6]. Gear fault signatures are sensed and acquired by two types of sensors: accelerometers and acoustic emission sensors [7]. Vibration signatures collected by the accelerometer from a gearbox carry enough fault-related information and can be used for efficient gear fault diagnosis [8]. Vibration signals obtained from a gearbox consist of meshing frequency harmonics, blended sideband frequencies, and other free oscillation frequencies. Therein, the meshing frequency harmonics and blended sideband frequencies are the fundamental defect-related frequencies that help in the process of identifying gear defects [9, 10]. The vibration signals obtained from a gearbox under variable speeds are complex and non-stationary; furthermore, the gear fault-related elements are often overwhelmed by the noise. To identify the fault symptoms in this complex vibration signal, the fault diagnosis technique tries to reduce the noise in the raw vibration signal [11]. In its raw form, the gearbox vibration signal contains various types of interference noises. The main sources for these interference noises are the interconnected systems, such as the electrical-electronic control and measuring systems, the mechanical systems (the influence of the mechanical resonances such as shaft, bearings, gears, etc. ), and background noise [12; 13]. The random behavior of these noises (i.e., random magnitudes, random appearances anywhere in the observed ranges of vibration signals) makes the noisy components dominant over the fault-related components in the vibration signal, and thus these noises overwhelm the fault-related components. To address this issue, a signal-processing technique, which can reduce the noise in the raw vibration signal, to highlight the fault-related meshing frequency harmonics and sidebands (fault-affiliated elements) for gearbox fault diagnosis in early stages is urgently needed. In the past, numerous signal processing techniques, such as Fourier transform (FT), envelope spectral analysis, Hilbert transform (HT), spectrogram or spectral analysis of a fixed timing-window Fourier transform (STHT), empirical mode decomposition (EMD), and wavelet-based spectral analysis (WA), have been developed for the processing of stationary and non-stationary complex signals [14; 15; 16; 17; 18; 19]. To enhance the performance of the basic signal processing techniques, hybrid signal processing techniques such as EMD and HT and EMD and WA have also been introduced [20; 21]. The vibration signatures obtained from a gearbox under faulty conditions are non-stationary. To obtain fault-related information from the non-stationary vibration signal, time-frequency domain techniques are applied. These techniques commonly use window-based filtering, digital filtering, threshold estimation, decomposition modes in the form of intrinsic mode functions, and wavelet-based transformation. Their fault identification efficiencies have been confirmed by classifying fault states (e.g., a fault-free state and a defective state) and denoising in some cases. In the case of a gearbox, the fault-related information is distorted by the hefty noise present in the raw signal. Therefore, noise reduction techniques before applying the time-frequency domain signal processing technique will be helpful for the identification of MDTF in gearboxes. [PERSON] et al.