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.

本文介绍了第三代有趣的工具，该工具专为时频形状（TFS）联合分析而创建。称为离散小波变换（DST-III），它改进了它的前任产品，即DST-I和DST-II，从而获得了几乎对称的主要小波函数，从而获得了几乎线性的相位滤波器组。在简要回顾了重要概念之后，详细说明了DST-III公式，并用数字示例进行了补充。此外，还介绍并讨论了原型模式匹配策略（与普通小波进行比较）以及尖峰排序应用程序。值得注意的是，小波展开用于提供非常简洁的信号表示，从而简化了时间和频率上的后续非线性信号分析，因此为科学和工程中的非平稳问题求解带来了优势。这样可以确保此新工具的有效性。