## 1 Introduction  
The problem of bearings local damage detection is widely discussed in the literature [1; 2; 3; 4]. In the case of constant speed, the task is defined as the detection of the periodic impulsive signals. The vibration under time-varying speed requires special treatment, see [5; 6], and will not be considered in this paper. The most popular approach is the envelope analysis and detection of fault frequencies in the spectrum of the envelope for a pre-filtered signal. The modified versions of the envelope are also known, e.g., squared envelope spectrum (SES) [2; 7], log-envelope spectrum (LES) [8; 9]. The filtration of a raw signal is used to select its informative part and avoid other spectral content not related to the local damage. Depending on the complexity of the structure of the signal one may use simple band-pass filtering, advanced decomposition via Empirical Mode Decomposition (EMD) [10; 11] or wavelet transform [12; 13; 14]. An optimal solution has been proposed by using Wiener filtering [15]. The filter coefficients could be optimized by the genetic algorithm proposed in [16]. The most popular approach is based on the spectral kurtosis as an informative frequency band (IFB) selector (filter characteristic). The kurtosis value is calculated for sub-signal at some narrow frequency band. As kurtosis is sensitive to outliers [17], one can select impulsive content at a given narrow frequency band and filter out other components. Kurtosis is the most intuitive statistic commonly used for machine diagnostics [18]. It has plenty of variations and extensions, e.g., the kurtogram [19]--which is a colored map, where the depth of the color values is proportional to the kurtosis value. [PERSON] showed that other statistics could also be used in such context [20]. Recently, many techniques for searching for optimal frequency band selection have appeared [21]. In the literature, one can also find methods which are based on the cyclostationary approach. Obviously, these algorithms are dedicated to the cyclic behavior identification for the real signals. In the classical approach of cyclostationary-based techniques the assumption of Gaussian noise is taken under consideration [7; 9; 22; 23; 24; 25; 26]. However, one can find the papers where the algorithms for the signals with non-Gaussian noise are proposed [27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. We refer also to the recent paper, where the new definition of the cyclostationary non-Gaussian signal is given, see [27] for more details. However, in this paper we do not consider the cyclostationary-based methods. One can also find other approaches for the IFB selection based on artificial intelligence [39; 40; 41]. However, there is still a need for new approaches that allow us to consistently handle restrictions linked to the amount of available data, specific type of noise, work specifications of the tested machine, etc. The idea of the paper is not to introduce a new technique which outperforms other methods for signals with the specific behavior, but to demonstrate the advantages and limitations of the selected algorithms. In many papers authors refer to other existing techniques to compare performance. However, due to lack of space in research papers, a novel technique can be compared to one or two other techniques for some specific signal, without a deep understanding of properties/limitations of each method. It makes real comparison difficult. Thus, the main goal of the paper is to compare the recently proposed methods for the IFB selection. The paper provides a comparative study of different methods used for local damage detection for real-life inspired benchmark signals (Gaussian White Noise, cyclic impulsive signals, non-cyclic impulsive signals with random amplitudes and locations of impulses and a mixture of all of them). The most complicated simulated signal considered in this paper, apart from the background noise, contains the non-cyclic impulses which are not informative.