Ten lectures on wavelets
Gabor Analysis and Algorithms: Theory and Applications
Gabor Analysis and Algorithms: Theory and Applications
Advances in Gabor Analysis
The analysis and design of windowed Fourier frame based multiple description source coding schemes
IEEE Transactions on Information Theory
The wavelet transform, time-frequency localization and signal analysis
IEEE Transactions on Information Theory
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Let A@?L^2(R) be at most countable, and p,q@?N. We characterize various frame-properties for Gabor systems of the formG(1,p/q,A)={e^2^@p^i^m^xg(x-np/q):m,n@?Zg@?A}in terms of the corresponding frame properties for the row vectors in the Zibulski-Zeevi matrix. This extends work by [Ron and Shen, Weyl-Heisenberg systems and Riesz bases in L"2(R^d). Duke Math. J. 89 (1997) 237-282], who considered the case where A is finite. As a consequence of the results, we obtain results concerning stability of Gabor frames under perturbation of the generators. We also introduce the concept of rigid frame sequences, which have the property that all sufficiently small perturbations with a lower frame bound above some threshold value, automatically generate the same closed linear span. Finally, we characterize rigid Gabor frame sequences in terms of their Zibulski-Zeevi matrix.