Contribution to the analysis of non-stationary and/or non-Gaussian signals.

Summary The wigner-ville transform (twv) is a well known tool in the analysis of non-stationary signals. Its non-linear structure is a source of interference between the components of the analyzed signal, which poses a problem when extracting the relevant information from the resulting image. Considered as a two-dimensional random process, this image is generally non-Gaussian. Thus, this transformation is the seat of three non-qualities: non-linearity, due to the operator, non-stationarity and non-Gaussianity, which affect the analyzed or produced signal. In this study, we are interested in the two non-qualities related to the signals: non-Gaussianity, where some techniques using statistics of order greater than two are discussed, and non-stationarity, which involves the wavelet transform as a second role. Finally, in an extended framework of twv, we meet simultaneously these two attributes. Another fundamental aspect of this work is a contribution to the transfer of signal processing techniques to the industrial domain, through the development of a non-stationary analysis software and its implementation in the vibratory analysis of an automotive engine.