Designing high-resolution time–frequency and time–scale distributions for the analysis and classification of non-stationary signals: a tutorial review with a comparison of features performance

Abstract

This paper deals with the problem of extracting information from non-stationary signals in the form of features that can be used for effective decision-making in both data analysis and machine learning for automatic classification systems. Suitable time–frequency (TF) and time–scale (TS) representations of such signals are reviewed for these purposes, and, the relationships between such TF and TS signal transformations is discussed. Both linear (atomic) decompositions and quadratic distributions are considered as well as other related methods such as fractional Fourier transform, polynomial Wigner–Ville distributions and time-varying order spectra. Current state-of-the-art methods are reviewed, and new results are presented including extensions of existing methods. Machine learning methodologies using TF/TS features can result in the design of systems that improve the classification of non-stationary signals. Using selected TF distributions (TFDs) and TS distributions (TSDs), the extraction of such TF/TS features is demonstrated on multi-channel recordings using channel fusion or feature fusion approaches. Extending the findings of previous studies, a TF/TS feature set is formed by including two complementary categories: signal related features and image features. The design of high-resolution TF/TS algorithms is then refined to account for issues of accuracy and robustness. Then, the desired TF/TS features are selected using different feature selection algorithms and compared with respect to the classification performance. Finally, other features from related methods are added, and comparisons performed. Improvements of up to 5% are obtained when using the chosen feature set after wrapper feature selection with channel feature fusion.