Topics in Nonabelian Harmonic Analysis and DSP Applications

Underlying most digital signal processing (DSP) algorithms is the group Z/N of integers modulo N , which is taken as the data indexing set. Recently, An and Tolimieri [1] considered a different class of index set mappings, which arise when the underlying group is nonabelian, and successfully apply them to 2D image data. Advantages of indexing signals with nonabelian groups are not limited to image data, but extend to audio signals as well. The present work provides an overview of DSP on finite groups and group algebras, “generalized translations,” and their consequences, “generalized convolutions.” Thereafter, some specific, simple examples of nonabelian-group indexing sets are discussed along with their practical implications.