Oversampled Wilson expansions
AuthorsHelmut Bölcskei, Karlheinz Gröchenig, Franz Hlawatsch, and Hans G. Feichtinger
ReferenceIEEE Signal Processing Letters, Vol. 4, No. 4, pp. 106-108, Apr. 1997.
AbstractRecently orthonormal Wilson bases with good time-frequency localization have been constructed by Daubechies, Jaffard, and Journé. We extend this construction to Wilson sets and frames with arbitrary oversampling (or redundancy). We state conditions under which dual Weyl-Heisenberg sets induce dual Wilson sets, and we formulate duality conditions in the time domain and frequency domain. We show that the dual frame of a Wilson frame has again Wilson structure, and that it is generated by the dual frame of the underlying Weyl-Heisenberg frame. The Wilson frame construction preserves the numerical properties of the underlying Weyl-Heisenberg frame while halving its redundancy.
KeywordsWilson expansions, Gabor expansions, Weyl-Heisenberg frames, oversampling
CommentsThere is a correction to this paper: Link to document
Download this document:
Copyright Notice: © 1997 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.