Journal article
Construction of smooth compactly supported windows generating dual pairs of gabor frames
Department of Applied Mathematics and Computer Science, Technical University of Denmark1
Scientific Computing, Department of Applied Mathematics and Computer Science, Technical University of Denmark2
Mathematics, Department of Applied Mathematics and Computer Science, Technical University of Denmark3
Let g be any real-valued, bounded and compactly supported function, whose integer-translates {Tkg}k∈ℤ form a partition of unity. Based on a new construction of dual windows associated with Gabor frames generated by g, we present a method to explicitly construct dual pairs of Gabor frames. This new method of construction is based on a family of polynomials which is closely related to the Daubechies polynomials, used in the construction of compactly supported wavelets.
For any k ∈ ℕ ∪ {∞} we consider the Meyer scaling functions and use these to construct compactly supported windows g ∈ Ck(ℝ) associated with a family of smooth compactly supported dual windows . For any n ∈ ℕ the pair of dual windows g, hn ∈ Ck(ℝ) have compact support in the interval [-2/3, 2/3] and share the property of being constant on half the length of their support.
We therefore obtain arbitrary smoothness of the dual pair of windows g, hn without increasing their support.
Language: | English |
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Year: | 2013 |
Pages: | 1350011 |
ISSN: | 17937183 and 17935571 |
Types: | Journal article |
DOI: | 10.1142/S1793557113500113 |
ORCIDs: | Christiansen, Lasse Hjuler and Christensen, Ole |