Application of Weyl-Heisenberg and affine-groups to scattering

Signals which are generated from radar echoes contain features which display time-like or frequency-like character. The time-like behavior is generated by strong specular returns while the frequency-like is caused by resonances. In order to study these phenomena it is often necessary to go beyond the normal frequency transform and pole extraction techniques and search for methods that treat time and frequency in the same footing. These techniques can be found in the coherent and affine state representation of signals. These representation are based on the structure of group theory and are generated by the symmetries of the underlying operations. Groups are characterized by a set of operations which form the multiplication table and representations which reproduce the group operations. The particular groups which are of interest are the continuous groups having unitary representations. A number of properties of these groups are global and are true for all applications. They are discussed in the article.