Gabor windows supported on [−1,1] and construction of compactly supported dual windows with optimal smoothness
نویسندگان
چکیده
منابع مشابه
A geometric construction of tight Gabor frames with multivariate compactly supported smooth windows
The geometry of fundamental domains of lattices was used by Han and Wang to construct multivariate Gabor frames for separable lattices. We build upon their results to obtain Gabor frames with smooth and compactly supported window functions. For this purpose we study pairs of lattices which have equal density and allow for a common compact and star-shaped fundamental domain. The results are then...
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Consider a continuous function g ∈ L2(R) that is supported on [−1, 1] and generates a Gabor frame with translation parameter 1 and modulation parameter 0 < b < 2N 2N+1 for some N ∈ N. Under an extra condition on the zeroset of the window g we show that there exists a continuous dual window supported on [−N, N]. We also show that this result is optimal: indeed, if b > 2N 2N+1 then a dual window ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2020
ISSN: 0021-9045
DOI: 10.1016/j.jat.2019.105304