Need for speed: Fast Stockwell transform (FST) with O(N) complexity

In this paper, we propose two fast, spline based, algorithms for computing the Stockwell Transform or the S-transform. It is a redundant, time-frequency representation that has certain desirable features which make it an attractive choice for signal analysis in different areas and motivated by its diverse applications, we seek to reduce its computational complexity. The S-transform bears an acute resemblance with the Gabor transform and can also be associated to the Continuous Wavelet Transform (CWT). Our formulation is based on the above mentioned connectivity with the two classical time-frequency tools. What singles out our approach is that it is recursive in nature and leads to a complexity of O(N) — for arbitrary scales, independent of scale of window.