###### Abstract  
Magnetic Barkhausen Noise (MBN) is a method being currently considered by many research and development centers, as it provides knowledge about the properties and current state of the examined material. Due to the practical aspects, magnetic anisotropy evaluation is one of such key areas. However, due to the non-stationary and stochastic nature of MBN, it requires searching for postprocessing procedures, allowing the extraction of crucial information on factors influencing the phenomenon. Advances in the field of the analysis of non-stationary signals by various transformations or decompositions resulting into new time- and frequency-related representations, allow the interpretation of complex sets of signals. Therefore, in this paper, several time-frequency transformations were used to analyze the data of MBN for the purpose of the magnetic anisotropy evaluation of electrical steel. The three main transform types with their modifications were considered and compared: the Short-Time Fourier Transform, the Continuous Wavelet Transform and the Smoothed Pseudo Wigner-Ville Transform. By using Exploratory Data Analysis methods and the parametrization of time-frequency representation, the qualitative and quantitative analysis was made. The STFT presented good performance on providing useful information on MBN changes while simultaneously leading to the lowest computational efforts. magnetic Barkhausen noise; grain-oriented electrotechnical steel; anisotropy; time-frequency representation; short-time Fourier transform; wavelet transform; Wigner-Ville distribution +
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time-scale (TS) representations allow one to obtain information, which may complement the knowledge obtained through the separate analysis carried out only in the time or frequency domains. TF representation analysis is used in many applications, requiring the processing of signal with time-varying signals to extract information. There are many transformations that allow one to process the signal from the time and frequency domains to the time-frequency representation (TFR). In this paper, the authors present the application of three main transformations groups, that came from different categories, along with their modifications. The first group includes the Short-Time Fourier Transform (STFT) related to the Fourier transform, based on the decomposition of the signal into components (represented by sine and cosine function with appropriate weights) for subsequent discrete time segments, so called windows of signal. This approach enables the determination of a sequence of short-time frequency characteristics in subsequent time intervals and the observation of changes in the content of the signal's components. The second group refers to the Continuous Wavelet Transform (CWT) related to the operation of matching (scaling and transition) a base function called a wavelet. Various base wavelet functions are used to provide different properties. Considering that linear transformations, such as the STFT and the CWT, constitute a certain local averaging of the characteristics, the method called Synchrosqueezed Transform (SST) was developed. It allows one to sharpen the transformed distributions in such a way that the operation remains invertible [6; 7; 8]. In the works introducing this transformation, one can find a reference to the Fourier Synchrosqueezed Transform (FSST) [6] and the Wavelet Synchrosqueezed Transform (WSST) [8] as well. The SST relocates the TFR and allows the outcome distribution to be sharpened. The synchrosqueezing operation is used for two purposes: to concentrate the TFR of a signal that consists of many components, and as a signal decomposition tool. The last analyzed group refers to a bilinear transformation--the Wigner-Ville Distribution (WVD). This transformation was further modified by adding a smoothing window in time and frequency modes to remove interferences resulting in a new version called the Smoothed Pseudo Wigner-Ville Distribution (SPWVD).