A Spectral Graph Fractional Stockwell Transform for Signal Analysis

In this paper, we introduce a fractional-order variant of the Stockwell transform, specifically designed for analyzing signals that can be represented in terms of a graph data structure and integrates the ideas of fractional Stockwell transform and spectral graph theory.The proposed transform is named the 'Spectral Graph Fractional Stockwell Transform' or 'SGFrST' for short.Fundamentally, SGFrST makes use of the graph spectral domain to extract the underlying connection patterns and network structure of complex systems.SGFrST essentially fills the gap between signal processing methods and spectral graph theory by providing a flexible instrument that allows for hitherto unheard-of levels of precision and efficiency when comprehending and interpreting signals on graph-based domains.To begin, we introduce the spectral graph Stockwell transform by modulating the graph wavelet transform.Subsequently, we extend this concept by incorporating the spectral graph wavelet operator alongside the fractional order, resulting in the SGFrST.We derive various mathematical properties associated with the SGFrST, including an inversion mechanism and an inner product theorem.The proposed transform demonstrates effective applicability across a spectrum of graph signal processing scenarios.Basically, this makes it possible to extract useful features from signals that are present on graph structures, which helps with a variety of tasks in domains such as the social sciences, neuroscience, image processing and telecommunications.These tasks include image restoration, anomaly detection, pattern identification, and classification.