Open Access
2013 Regularity of Dual Gabor Windows
Ole Christensen, Hong Oh Kim, Rae Young Kim
Abstr. Appl. Anal. 2013: 1-8 (2013). DOI: 10.1155/2013/747268


We present a construction of dual windows associated with Gabor frames with compactly supported windows. The size of the support of the dual windows is comparable to that of the given window. Under certain conditions, we prove that there exist dual windows with higher regularity than the canonical dual window. On the other hand, there are cases where no differentiable dual window exists, even in the overcomplete case. As a special case of our results, we show that there exists a common smooth dual window for an interesting class of Gabor frames. In particular, for any value of K ℕ, there is a smooth function h which simultaneously is a dual window for all B-spline generated Gabor frames { E m b T n B N ( x / 2 ) } m , n for B-splines B N of order N = 1 , , 2 K + 1 with a fixed and sufficiently small value of b .


Download Citation

Ole Christensen. Hong Oh Kim. Rae Young Kim. "Regularity of Dual Gabor Windows." Abstr. Appl. Anal. 2013 1 - 8, 2013.


Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 07095322
MathSciNet: MR3108630
Digital Object Identifier: 10.1155/2013/747268

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
Back to Top