Abstract
In this article, we introduce the structure of wave packet groups over finite cyclic groups, as the finite non-Abelian groups consist of cyclic dilations, translations, and modulations. Then, we present the notion of wave packet representations on wave packet groups. As an application of wave packet representations, we study constructive and analytic properties of the cyclic wave packet transforms associated to these representations. Finally, we apply these techniques in the case of some finite cyclic groups.
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