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Gabor dual spline windows. (English) Zbl 1174.42038
Author’s abstract: A method is presented for constructing dual Gabor window functions that are polynomial splines. The spline windows are supported in $[-1,1]$, with a knot at $x=0$, and can be taken $C^m$ smooth and symmetric. The translation and modulation parameters satisfy $a=1$ and $0<b\leqslant 1/2$. The full range $0<ab<1$ is handled by introducing an additional knot. Many explicit examples are found.

42C15General harmonic expansions, frames
Full Text: DOI
[1] Christensen, O.: An introduction to frames and Riesz bases, (2003) · Zbl 1017.42022
[2] Christensen, O.: Frames and bases: an introductory course, Appl. numer. Harmon. anal. (2008) · Zbl 1152.42001
[3] Christensen, O.: Pairs of dual Gabor frame generators with compact support and desired frequency localization, Appl. comput. Harmon. anal. 20, 403-410 (2006) · Zbl 1106.42030 · doi:10.1016/j.acha.2005.10.003
[4] Christensen, O.; Kim, R. Y.: Pairs of explicitly given dual Gabor frames in $L2(Rd)$, J. Fourier anal. Appl. 12, 243-255 (2006) · Zbl 1096.42015 · doi:10.1007/s00041-005-5052-3
[5] O. Christensen, R.Y. Kim, On dual Gabor frame pairs generated by polynomials, J. Fourier Anal. Appl., in press · Zbl 1210.42048 · doi:10.1007/s00041-009-9074-0
[6] Christensen, O.; Laugesen, R. S.: Approximately dual frame pairs in Hilbert spaces and applications to Gabor frames, preprint, (2008)
[7] Daubechies, I.; Grossmann, A.; Meyer, Y.: Painless nonorthogonal expansions, J. math. Phys. 27, 1271-1283 (1986) · Zbl 0608.46014 · doi:10.1063/1.527388
[8] , Appl. numer. Harmon. anal. (1998)
[9] Gröchenig, K.: Foundations of time -- frequency analysis, Appl. numer. Harmon. anal. (2001) · Zbl 0966.42020
[10] Janssen, A. J. E.M.: The duality condition for Weyl -- Heisenberg frames, Appl. numer. Harmon. anal., 33-84 (1998) · Zbl 0890.42006
[11] Lemvig, J.: Constructing pairs of dual bandlimited framelets with desired time localization, Adv. comput. Math. 30, No. 3, 231-247 (2009) · Zbl 1166.42020 · doi:10.1007/s10444-008-9066-7