## 1 Introduction  
Partial discharge (PD) measurements have been made on electrical equipment insulation for many years and proved to be a sensitive means of insulation condition assessment and fault diagnosis [1; 2; 3; 4; 5; 6; 7]. However, electrical equipment operates in a strong electromagnetic environment, and PD on-line measurements are extremely affected and hampered by electrical noise [2]. In addition, it is very common that multiple PD sources present simultaneously in insulation systems, especially for large generators. PD signals suffer from different degrees of attenuation when propagating from the discharge site to detector location through various paths, resulting in a low signal to noise ratio (SNR) of the measured signal. PD signals may be overwhelmed by severe noise and are difficult to be effectively extracted from the noisy signal, affecting the accurate assessment of insulation conditions. The waveforms of PD pulses are important for PD pulses clustering and PD source identification. Therefore, it is important to eliminate noise as much as possible to increase the SNR, to minimize signal distortions and preserve the PD waveforms. Wavelet transform is an efficient mathematics tool and is utilized for PD signal denoising due to the unique ability to identify singularity signal in both time and frequency domains. Mother wavelet selection,decomposition level determination, and threshold estimation together with threshold function are the major problems that influence the denoising effect [8]. Great efforts have been made on optimum mother wavelet selection methods. In the early stage of PD denoising, the selection of the optimum mother wavelet is typically handled based on the experience of the researchers or by trial and error; the selection methods are different in literature and can only perform well in their own environments [9; 10; 11]. A specific criterion is urgently needed for the optimum mother wavelet selection. To this end, numerous techniques have been proposed for the PD denoising. The correlation based wavelet selection methods (CBWS) are made with the purpose of maximizing the correlation between the original PD signal and the wavelet function chosen from a library of wavelets [12; 13]. Nevertheless, the real PD signal shape is unknown in most cases and CBWS methods are time-consuming. An alternative is to select the optimum mother wavelet based on the correlation between the coefficients and the measured signals [14; 15]. To simplify the calculation of correlation, the dynamic time warping (DTW) method was introduced [16]. An attempt to improve the CBWS method by replacing DWT with stationary wavelet transform is proposed in [17] at the expense of a sharp increase in time consumption. However, waveforms of measured pulses depend on the types and locations of PD sources, propagation paths of PD pulses, and the response characteristics of detectors. It is difficult for CBWS to obtain a typical pulse waveform to represent all PD pulses. Besides, when noised PD signal is adopted to calculate the correlation, improper selection of mother wavelet by these schemes may be incurred, especially for signals with low SNR. In [8], energy based wavelet selection (EBWS) is proposed and the optimum mother wavelet is selected as the one generating an approximation with the largest energy at each scale, while it may suffer more component loss and lead to less-than-desirable results when the energy mainly locates in the detail coefficients. With the purpose to maximize the energy concentrating on the sub-band that the signal frequency distributes, the energy and entropy ratio based wavelet selection [18], a new energy based wavelet selection (NewEBWS) [17], and signal-to-noise ratios based wavelet selection (SNRBWS) [19] are proposed in succession. SNRBWS is focused on the maximum coefficient of the noised signal at each scale, but may get worse results when there are massive small pulses in the noised signal. The decomposition level is important to the denoising results.