The Discrete Stockwell Transforms for Infinite-Length Signals and Their Real-Time Implementations

The various forms of the Stockwell transforms (ST) introduced in the literature have been developed for off-line signal processing on finite-length signals. However, in many applications such as audio, medical or radar signal processing, signals to be analyzed are of large sizes or received in real-time, time-frequency representations of such a signal cannot be calculated using the entire signal. The common approach is to calculate the spectrum segment-by-segment. This may result obvious boundary effects or lose absolute-referenced phase information in their time-frequency representations. In this paper, new formulations of the discrete ST for infinite-length signals are proposed. Based on the new definitions, fast algorithms are implemented using the fast Fourier transform. Our proposed computational schemes make it possible to process an infinite-length/large size signal segment-by-segment at low computational cost without any boundary effects. More importantly, the absolute-referenced phase information is reserved in this approach. These properties make the infinite-length STs more suitable for real-time signal processing.