On general frame decompositions
- 1 January 1995
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 16 (9-10) , 1181-1191
- https://doi.org/10.1080/01630569508816668
Abstract
We provide a characterization and construction of general frame decompositions. We show that generating all duals for a given frame amounts to finding left inverses of an one-to-one mapping. A general parametric and algebraic formula for all duals is derived. An application of the theory to Weyl-Heisenberg (WH) frames is discussed. Besides the (usual) dual frame that preserves the translation and modulation structure, we construct a class of duals that attain such a structure. We also show constructively that there are duals to WH frames which are not the translation and modulation of a single function.Keywords
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