Wavelets: a general overview

Summary form only given, as follows. The Heisenberg group and its representation theory plays an important role in the theory of Gabor expansions, ambiguity functions and Wigner distributions and wavelets built from translations in time and frequency. A multiplicative Heisenberg group whose representation theory can be used to study affine group wavelets and wideband ambiguity functions is defined. The standard Zac transform can be interpreted as an intertwining operator between two unitary representations of the Heisenberg group. A multiplicative Zac transform that plays an analogous role for the multiplicative Heisenberg group is constructed