Abstract
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.
Original language | English |
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Journal | Advances in Computational Mathematics |
Volume | 36 |
Issue number | 4 |
Pages (from-to) | 525-545 |
ISSN | 1019-7168 |
DOIs | |
Publication status | Published - 2012 |
Keywords
- Gabor frame
- Compactly supported window
- Compactly supported dual window