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Viser: The Abc-Problem for Gabor Systems
The Abc-Problem for Gabor Systems
Xin-Rong Dai og Qiyu Sun
(2016)
Sprog: Engelsk
American Mathematical Society
1.297,00 kr.
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Detaljer om varen
- Paperback: 99 sider
- Udgiver: American Mathematical Society (Oktober 2016)
- Forfattere: Xin-Rong Dai og Qiyu Sun
- ISBN: 9781470420154
A longstanding problem in Gabor theory is to identify time-frequency shifting lattices $a\mathbb{Z}\times b\mathbb{Z}$ and ideal window functions $\chi_I$ on intervals $I$ of length $c$ such that $\{e^{-2\pi i n bt} \chi_I(t- m a):\ (m, n)\in \mathbb{Z}\times \mathbb{Z}\}$ are Gabor frames for the space of all square-integrable functions on the real line. In this paper, the authors create a time-domain approach for Gabor frames, introduce novel techniques involving invariant sets of non-contractive and non-measure-preserving transformations on the line, and provide a complete answer to the above $abc$-problem for Gabor systems.
Introduction
Gabor frames and infinite matrices Maximal invariant sets Piecewise linear transformations Maximal invariant sets with irrational time Shifts Maximal invariant sets with rational time shifts The $abc$-problem for Gabor systems
Appendix A. Algorithm
Appendix B. Uniform sampling of signals in a shift-invariant space Bibliography
Gabor frames and infinite matrices Maximal invariant sets Piecewise linear transformations Maximal invariant sets with irrational time Shifts Maximal invariant sets with rational time shifts The $abc$-problem for Gabor systems
Appendix A. Algorithm
Appendix B. Uniform sampling of signals in a shift-invariant space Bibliography
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