Gabor Wigner Transform (GWT) is a composition of two time-frequency planes (Gabor Transform (GT) and Wigner Distribution (WD)), and hence GWT takes the advantages of both transforms (high resolution of WD and cross-terms free GT). In multi-component signal analysis where GWT fails to extract auto-components, the marriage of signal processing and image processing techniques proved their potential to extract autocomponents. The proposed algorithm maintained the resolution of auto-components. This work also shows that the Fractional Fourier Transform (FRFT) domain is a powerful tool for signal analysis. Performance analysis of modified fractional GWT reveals that it provides a solution of cross-terms of WD and blurring of GT.

In this paper, a modified form of the Gabor Wigner Transform (GWT) has been proposed. It is based on adaptive thresholding in the Gabor Transform (GT) and Wigner Distribution (WD). The modified GWT combines the advantages of both GT and WD and proves itself as a powerful tool for analyzing multi-component signals. Performance analyses of the proposed distribution are tested on the examples, show high resolution and crossterms suppression. To exploit the strengths of GWT, the signal synthesis technique is used to extract amplitude varying auto-components of a multi-component signal. The proposed technique improves the readability of GWT and proves advantages of combined effects of these signal processing techniques.

1) Background: the modeling, characterization, transformation and propagation of high-power CW laser beams in optical (including fiberoptic) trains and in the atmosphere have become hot topics in laser science and engineering in the past few years. Single-mode output is mandatory for high-power CW laser applications in the military field. Moreover, an unstationary, dynamic operation regime is typical. Recognized devices and procedures for laser-beam diagnostics could not be directly applied because of dynamic behavior and untypical non-Gaussian profiles. 2) Methods: the Wigner transform approach was proposed to characterize dynamically variable high-power CW laser beams with significant deterministic aberrations. Wavefront-sensing measurements by means of the Shack-Hartmann method and decomposition into an orthogonal Zernike basis were applied. 3) Results: deterministic aberration as a result of unstationary thermal-optic effects depending on the averaged power of the laser output was found. Beam quality determined via the Wigner approach was changed in the same way as the measurements of the beam diameter in the far field. 4) Conclusions: such an aberration component seems to be the main factor causing degradation in beam quality and in brightness of high-power CW laser beams.

The one-dimension frequency analysis based on DFT (Discrete FT) is sufficient in many cases in detecting power disturbances and evaluating power quality (PQ). To illustrate in a more comprehensive manner the character of the signal, time-frequency analyses are performed. The most common known time-frequency representations (TFR) are spectrogram (SPEC) and Gabor Transform (GT). However, the method has a relatively low time-frequency resolution. The other TFR: Discreet Dyadic Wavelet Transform (DDWT), Smoothed Pseudo Wigner-Ville Distribution (SPWVD) and new Gabor-Wigner Transform (GWT) are described in the paper. The main features of the transforms, on the basis of testing signals, are presented.