信号表示统一设想初探

Unification of signal transforms on groups: An introduction

信号处理的基础是信号表示(或称信号变换).构造新的信号表示方法是信号处理中的关键问题.本文提出信号表示统一设想,试图从群结构层面探索现有名目繁多的信号表示之间的内在关联性,以达到统一现有变换的目的.设想以"元素周期表"进行类比,旨在构造一种由"群格"组成的"群表",用以给出现有信号表示在"群表"上的统一形式,并根据该统一形式所揭示的现有变换在群上的内在关系,期望定义出若干具备所需性质和应用价值的新的变换.

The foundation of signal processing is the signal representation （or signal transform）, and therefore, constructing the new signal representations is no doubt an important topic in signal processing community. This paper proposes an assumption of unified signal representations, attempting to explore the intrinsic rela- tionship among numerous existing signM representations in the structural level of group theory. By analogy with Mendeleev＇s Periodic Table of Elements, the assumption aims at unifying available signal representations on groups via the so-called ＂group table＂ built by the ＂group blocks＂, and defining some new specific and valuable signal representations with required properties in accordance with the ＂group table＂.