The abc-problem for Gabor systems / Xin-Rong Dai, Qiyu Sun.

The abc-problem for Gabor systems /

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 al...

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Bibliographic Details
Main Authors: Dai, Xin-Rong, 1971- (Author), Sun, Qiyu, 1966- (Author)
Format: Electronic eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, 2016.
Series:Memoirs of the American Mathematical Society ; no. 1152.
Subjects:
Wavelets (Mathematics)
Gabor transforms.
Matrices.
Online Access: Full text (Wentworth users only)
Local Note:ProQuest Ebook Central
Table of Contents:
  • 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.

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