On the time-frequency content of Weyl-Heisenberg frames generated from odd and even functions [signal representation applications]

This work discusses the time-frequency content of frames, especially of Weyl-Heisenberg frames. We begin by showing that the sum of the time-frequency contents of all the functions in a set being always positive is a sufficient condition for this set of functions to generate a frame. It is then derived that for Weyl-Heisenberg frames {E_mbT_nag(t)}_n,mεz of an even function g(t) the maxima are placed at (na, mb) in the time-frequency domain and the minima at (na+a/2, mb+b/2); whereas for an odd function g(t) the maxima are placed at (na, mb+b/2) and the minima at (na+a/2, mb). This indicates effective ways to, for a given increase in the cardinality of the frame, obtain "tighter" frame bounds.