Regularity of Dual Gabor Windows

Title
Regularity of Dual Gabor Windows
Author(s)
김래영Ole Christensen[Ole Christensen]김홍오[김홍오]
Keywords
FRAMES
Issue Date
201309
Publisher
HINDAWI PUBLISHING CORPORATION
Citation
ABSTRACT AND APPLIED ANALYSIS
Abstract
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 is an element of N, there is a smooth function h which simultaneously is a dual window for all B-spline generated Gabor frames {EmbTnBN(x/2)}(m,n is an element of N) for B-splines B-N of order N = 1,..., 2K + 1 with a fixed and sufficiently small value of b.
URI
http://hdl.handle.net/YU.REPOSITORY/29050http://dx.doi.org/10.1155/2013/747268
ISSN
1085-3375
Appears in Collections:
이과대학 > 수학과 > Articles
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