Gabor windows supported on [ -aEuro parts per thousand 1, 1] and dual windows with small support

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Consider a continuous function g aaEuro parts per thousand L (2)(a"e) that is supported on [ -aEuro parts per thousand 1, 1] and generates a Gabor frame with translation parameter 1 and modulation parameter 0 < b < 2N/2N+1 for some N epsilon N center dot. 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 supported on [ -N, N] does not exist. In the limit case b = 2N/2N+1 a dual window supported on [-N, N] might exist, but cannot be continuous.
Publisher
SPRINGER
Issue Date
2012-05
Language
English
Article Type
Article
Keywords

FRAMES; BASES

Citation

ADVANCES IN COMPUTATIONAL MATHEMATICS, v.36, no.4, pp.525 - 545

ISSN
1019-7168
DOI
10.1007/s10444-011-9189-0
URI
http://hdl.handle.net/10203/103034
Appears in Collection
MA-Journal Papers(저널논문)
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