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Wilson frames for ℂL with general lattices

In digital signal and image processing one can only process discrete signals of finite length, and the space ℂL is the preferred setting. Recently, Kutyniok and Strohmer constructed orthonormal Wilson bases for ℂL with general lattices of volume L 2 (L even). In this paper, we extend this construction to Wilson frames for ℂL with general lattices of volume L 2K, where K ∈ ℕ and L ∈ 2Kℕ. We obtain a necessary and sufficient condition for two sequences having Wilson structure to be dual frames for ℂL. When the window function satisfies some symmetry property, we obtain a characterization of a Wilson system to be a tight frame for ℂL, show that a Wilson frame for ℂL can be derived from the underlying Gabor frame, and that the dual frame having Wilson structure can also be derived from the canonical Gabor dual of the underlying Gabor frame.