Journal article
Gabor windows supported on [ − 1, 1] and dual windows with small support
Consider a continuous function g ∈ L 2(ℝ) that is supported on [ − 1, 1] and generates a Gabor frame with translation parameter 1 and modulation parameter 0 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 b2N2N+1 then a dual window supported on [ − N, N] does not exist. In the limit case b=2N2N+1 a dual window supported on [ − N, N] might exist, but cannot be continuous.
Language: | English |
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Publisher: | Springer US |
Year: | 2012 |
Pages: | 525-545 |
ISSN: | 15729044 and 10197168 |
Types: | Journal article |
DOI: | 10.1007/s10444-011-9189-0 |
ORCIDs: | Christensen, Ole |