Stockwell S-Transform

The MATLAB implementation of the Stockwell S-Transform effectively integrates characteristics of both Fast Fourier Transform (FFT) and wavelet transforms, providing a comprehensive signal analysis tool. The Stockwell S-Transform is a time-frequency analysis method capable of capturing instantaneous frequency information and local frequency characteristics of signals. Through transformation between time and frequency domains, it visualizes signal variations across different time points and frequency bands, enabling better understanding of signal properties and structures. In MATLAB implementation, the S-Transform can be achieved using dedicated functions and algorithms that convert signals into time-frequency representations, which can then be further analyzed and processed. The core algorithm involves calculating localized spectrum using Gaussian windows with frequency-dependent resolution, where frequency-dependent scaling maintains progressive resolution similar to wavelet transforms while preserving absolute phase information like FFT. This implementation typically utilizes MATLAB's built-in FFT operations for computational efficiency, with optional parameters controlling window widths and frequency sampling intervals. Consequently, the MATLAB implementation of Stockwell S-Transform offers enhanced and precise tools for signal processing and analysis applications.