A geometric construction of tight multivariate Gabor frames with compactly supported smooth windows. (English) Zbl 1242.42028
Han and Wang have constructed Gabor systems with windows that are characteristic functions of fundamental domains for pairs of lattices. The authors indicate the main drawback of that approach: the constructed functions are discontinuous and may not even decay at infinity. In order to overcome this difficulty, one has to consider window functions in \(C_c(\mathbb R^d)\) whose support extends beyond the fundamental domain of lattice in question.
Building on the work of Han and Wang the authors provide in Theorem 4.2 sufficient conditions for obtaining Gabor frames with smooth and compactly supported window functions.
As an application, the authors show that one can construct such window functions for lattices which have star-shaped fundamental domains.
In the concluding section the authors provide several concrete examples which illustrate their technique in the case \(d=2\).
Building on the work of Han and Wang the authors provide in Theorem 4.2 sufficient conditions for obtaining Gabor frames with smooth and compactly supported window functions.
As an application, the authors show that one can construct such window functions for lattices which have star-shaped fundamental domains.
In the concluding section the authors provide several concrete examples which illustrate their technique in the case \(d=2\).
Reviewer: Damir Bakić (Zagreb)
MSC:
| 42C15 | General harmonic expansions, frames |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
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