Discrete Gabor frames in $\ell ^2(\mathbb {Z}^d)$

DOI10.1090/S0002-9939-2013-11875-7zbMath1278.42040MaRDI QIDQ2846909

Jerry Lopez, De Guang Han

Publication date: 4 September 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

frameWeyl-Heisenberg framediscrete Gabor frame

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) General harmonic expansions, frames (42C15)

Related Items (13)

On partition of unities generated by entire functions and Gabor frames in \( L^2(\mathbb R^d) \) and \(\ell^2(\mathbb Z^d)\) ⋮ Directional frames for image recovery: multi-scale discrete Gabor frames ⋮ Discrete vector-valued nonuniform Gabor frames ⋮ Pairwise orthogonal frames generated by regular representations of LCA groups ⋮ Orthogonality of a pair of frames over locally compact abelian groups ⋮ Discrete Gabor frames and \(K\)-discrete Gabor frames ⋮ Nonstationary frames of translates and frames from the Weyl–Heisenberg group and the extended affine group ^* ⋮ Gabor frames in \(\ell^2(\mathbb{Z})\) and linear dependence ⋮ Finite dual \(\mathbf{g} \)-framelet systems associated with an induced group action ⋮ Construction of \(P^{th}\)-stage nonuniform discrete wavelet frames ⋮ Translation partitions of unity, symmetry properties, and Gabor frames ⋮ Reproducing formulas for generalized translation invariant systems on locally compact abelian groups ⋮ Vector-valued weak Gabor dual frames on discrete periodic sets

Cites Work

• The existence of tight Gabor duals for Gabor frames and subspace Gabor frames
• Gabor analysis over finite Abelian groups
• Discrete Gabor transforms: The Gabor-Gram matrix approach
• Discrete Gabor expansion of discrete-time signals in \(l^ 2(\mathbb{Z})\) via frame theory
• Grassmannian frames with applications to coding and communication
• Equal-norm tight frames with erasures
• The uniqueness of the dual of Weyl--Heisenberg subspace frames
• On Coset Representatives in Groups
• Frame representations and Parseval duals with applications to Gabor frames
• Frames, bases and group representations
• On Representatives of Subsets
• Approximations for Gabor and wavelet frames
• Classification of Finite Group-Frames and Super-Frames
• Lattice tiling and the Weyl-Heisenberg frames
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