On Matrix Fourier Multipliers for Semi-orthonormal Binary Framelets and Perturbation of Gabor Frames and Applications

DOI

10.2991/icmra-15.2015.276How to use a DOI?

Keywords

Bivariate Gabor frames; dual Gabor frames; Banach space; time-frequency analysis; wavelet transfers; filter banks; paraunitary operator

Abstract

Mechanical engineering is the profession in which knowledge of the mathe -matical and natural sciences. The concept for matrix Fourier multipliers concerning bivariate tight multi-wavelet frames is introduced in this paper. Based on matrix theory, a sufficient and necessary condition for a matrix–valued function, which becomes matrix Fourier multipliers for bivariate tight multi-wavelet frames is provided. The existence of bivariate Gabor frames with compact support is discussed. Sufficient conditions for irregular bivariate Gabor system to be frames are presented by means of frame multiresolution analysis and paraunitary vector filter bank theory.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Qingjiang Chen
AU  - Bingzhe Wei
AU  - Yanbo Zhang
PY  - 2015/04
DA  - 2015/04
TI  - On Matrix Fourier Multipliers for Semi-orthonormal Binary Framelets and Perturbation of Gabor Frames and Applications
BT  - Proceedings of the 3rd International Conference on Mechatronics, Robotics and Automation
PB  - Atlantis Press
SP  - 1428
EP  - 1431
SN  - 2352-538X
UR  - https://doi.org/10.2991/icmra-15.2015.276
DO  - 10.2991/icmra-15.2015.276
ID  - Chen2015/04
ER  -