Nearly symmetric orthogonal wavelets for time-frequency-shape joint analysis: Introducing the discrete shapelet transform's third generation (DST-III) for nonlinear signal analysis

Abstract

This article introduces the third generation of an interesting tool created for time-frequency-shape (TFS) joint analysis. Called Discrete Shapelet Transform (DST-III), it improves both its predecessors, i.e., DST-I and DST-II, in such a way that nearly symmetric major shapelet functions, and consequently almost linear-phase filterbanks, are obtained. Following a brief review on important concepts, the DST-III formulation is specified in detail and complemented with a numerical example. In addition, a prototype pattern matching strategy, where a comparison with ordinary wavelets takes place, and a spike sorting application are also presented and discussed. Notably, wavelet expansions use to provide very concise signal representations, thus simplifying subsequent nonlinear signal analysis in both time and frequency and, consequently, bringing advantages for non-stationary problem solving in science and engineering. This reassures the efficacy of this new tool.