Generalized Fourier Transforms
In the process of specifying and modelling data structures for wide classes of real-time applications (signal-processing, pattern recognition, communications engineering) it has become a helpful tool to choose these structures as algebras which allow a group of automorphisms acting on the set of data.
With this data algebras being suchwise enhanced many of the above mentioned applications find a natural description.
In this lecture we will show that this description can successfully be used for a unifying approach to fast algorithms for many applications e.g. by reproducing the known classes of FFT's. The concept of the generalized Fourier-Transform can also be used in this context to generate such algorithms almost mechanically, as we will show in some examples.
KeywordsNormal Subgroup Irreducible Representation Cyclic Group Solvable Group Finite Abelian Group
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