Classifying Tight Weyl-Heisenberg Frames

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A Weyl-Heisenberg frame for L²(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g for which all translates and modulates of g form an orthonormal basis for L²(R). There are a number of consequences of this classification, including a simple direct classification of the alternate dual frames to a WH-frame (A result originally due to Janssen).