The S-transform (a multi-scale Fourier transform) reveals the temporal variation of frequency content in a signal. It has been successfully used in various fields from geophysics to biomedicine. The S-transform and its variations in the current literature are defined in the context of finite-length signals. However, in many applications such as audio or real-time signal processing, the size of the signal is large or infinite. Therefore, in this paper, we present new formula of the discrete S-transforms for infinite-length signals. Our new computational scheme makes it possible to process a long or infinite-length signal at low computational cost without boundary effects and are suitable to be realized in real-time systems.
This is a joint work with Yusong Yan.