On rationally oversampled Weyl-Heisenberg frames

Abstract

We relate the matrix elements of the linear systems, arising in the Zibulski-Zeevi method for computing dual functions for rationally oversampled Weyl-Heisenberg frames, to the Wexler-Raz method for computing dual functions. We give a necessary and sufficient condition for two functions g, γ having a frame upper bound to be dual in terms of their Zak transforms, we characterize the minimal dual function °γ and we present a necessary and sufficient condition, in terms of the Zak transform, for a function g so that the Tolimieri-Orr condition A is satisfied. The latter result is used to show that a g generating a rationally oversampled Weyl-Heisenberg frame and satisfying condition A has a minimal dual function that satisfies condition A as well.