OVERSAMPLED WILSON EXPANSIONS

Recently orthonormal Wilson bases with good time-frequency localizatio n have been constructed by Daubechies, Jaffard, and Journe. We extend this construction to Wilson sets and frames with arbitrary oversamplin g (or redundancy). We state conditions under which dual Weyl-Heisenber g (WH) sets induce dual Wilson sets, and we formulate duality conditio ns in the time domain and frequency domain. We show that the dual fram e of a Wilson frame has again Wilson structure, and that it is generat ed by the dual frame of the underlying Weyl-Heisenberg frame. The Wils on frame construction preserves the numerical properties of the underl ying Weyl-Heisenberg frame while halving its redundancy.