Discrete Stockwell Transform and Reduced Redundancy Versions from Frame Theory Viewpoint

The present work gives an interpretation of the discrete Stockwell transform (DST) from the theory of frame (TOF) perspective, showing first of all that the complete set of expansion functions of the DST is a frame. Starting from this interpretation, two versions of the DST are derived that allow to get a reduced redundancy representation of the original time series, when compared to the complete DST: the first method is based on a dyadic tiling of the time-frequency plane and leads to a perfect reconstruction representation using O(N) coefficients, whilst the second method is inspired by the matching pursuit technique and only provides an approximate representation of the original time series, but achieves better performances in terms of compactness, useful property in many practical applications.