Weyl-Heisenberg systems

For a finite abelian group A and g ∈ L(A), we define the concept of a translate of g by an element in A × A* and form systems of functions in L(A) by translates of g over subgroups Δ of A × A*. Such systems are called Weyl-Heisenberg (W-H) systems and expansions of signals over W-H systems are called W-H expansions. W-H expansions naturally embed into many time-frequency constructions and distributions resulting in significant simplification in the form of basic formulas and in the interpretation of computations.