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Wilson frames for ℂL with general lattices
- Source :
- International Journal of Wavelets, Multiresolution and Information Processing. 14:1650055
- Publication Year :
- 2016
- Publisher :
- World Scientific Pub Co Pte Ltd, 2016.
-
Abstract
- In digital signal and image processing one can only process discrete signals of finite length, and the space [Formula: see text] is the preferred setting. Recently, Kutyniok and Strohmer constructed orthonormal Wilson bases for [Formula: see text] with general lattices of volume [Formula: see text] ([Formula: see text] even). In this paper, we extend this construction to Wilson frames for [Formula: see text] with general lattices of volume [Formula: see text], where [Formula: see text] and [Formula: see text]. We obtain a necessary and sufficient condition for two sequences having Wilson structure to be dual frames for [Formula: see text]. When the window function satisfies some symmetry property, we obtain a characterization of a Wilson system to be a tight frame for [Formula: see text], show that a Wilson frame for [Formula: see text] can be derived from the underlying Gabor frame, and that the dual frame having Wilson structure can also be derived from the canonical Gabor dual of the underlying Gabor frame.
- Subjects :
- Pure mathematics
Computer Science::Information Retrieval
High Energy Physics::Lattice
Applied Mathematics
010102 general mathematics
Frame (networking)
Astrophysics::Instrumentation and Methods for Astrophysics
Structure (category theory)
Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)
Image processing
02 engineering and technology
Space (mathematics)
01 natural sciences
Digital signal (signal processing)
Window function
Signal Processing
0202 electrical engineering, electronic engineering, information engineering
Computer Science::General Literature
020201 artificial intelligence & image processing
Orthonormal basis
0101 mathematics
Symmetry (geometry)
Information Systems
Mathematics
Subjects
Details
- ISSN :
- 1793690X and 02196913
- Volume :
- 14
- Database :
- OpenAIRE
- Journal :
- International Journal of Wavelets, Multiresolution and Information Processing
- Accession number :
- edsair.doi...........5e29ef8528e71ea3c7d279da399aff1f