Gabor's signal expansion and a modified Zak transform for a quincunx-type sampling geometry

M.J. Bastiaans; A.J. Leest, van

doi:10.1109/ISSPA.1999.818162

Gabor's signal expansion and a modified Zak transform for a quincunx-type sampling geometry

M.J. Bastiaans, A.J. Leest, van

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

Gabors signal expansion and the Gabor transform are formulated on a quincunx lattice instead of on the traditional rectangular lattice; the representation of the quincunx lattice is based on the rectangular lattice via either a shear operation or a rotation operation. A modified Zak transformation is defined with the help of which Gabor's signal expansion and the Gabor transform can be brought into product forms that are identical to the ones that are well known for the rectangular sampling geometry. The shear operation on the lattice is associated with an operation on the synthesis and the analysis window, consisting of a multiplication by a quadratic-phase function. Following this procedure, the well-known biorthogonality condition for the window functions in the rectangular sampling geometry can be directly translated to the quincunx case.

Original language	English
Title of host publication	Proc. ISSPA '99, Fifth International Symposium on Signal Processing and its Applications, Brisbane, Australia
Editors	M. Deriche, B. Boashash, W.W. Boles
Place of Publication	Brisbane, QLD, Australia
Publisher	Queensland University of Technology
Pages	259-262
ISBN (Print)	1 86435 451 8
DOIs	https://doi.org/10.1109/ISSPA.1999.818162
Publication status	Published - 1999
Event	ISSPA '99, Fifth International Symposium on Signal Processing and its Applications - Brisbane, Australia Duration: 22 Aug 1999 → 25 Aug 1999

Conference

Conference	ISSPA '99, Fifth International Symposium on Signal Processing and its Applications
Country	Australia
City	Brisbane
Period	22/08/99 → 25/08/99

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10.1109/ISSPA.1999.818162

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Bastiaans, M. J., & Leest, van, A. J. (1999). Gabor's signal expansion and a modified Zak transform for a quincunx-type sampling geometry. In M. Deriche, B. Boashash, & W. W. Boles (Eds.), Proc. ISSPA '99, Fifth International Symposium on Signal Processing and its Applications, Brisbane, Australia (pp. 259-262). Queensland University of Technology. https://doi.org/10.1109/ISSPA.1999.818162

Bastiaans, M.J. ; Leest, van, A.J. / Gabor's signal expansion and a modified Zak transform for a quincunx-type sampling geometry. Proc. ISSPA '99, Fifth International Symposium on Signal Processing and its Applications, Brisbane, Australia. editor / M. Deriche ; B. Boashash ; W.W. Boles. Brisbane, QLD, Australia : Queensland University of Technology, 1999. pp. 259-262

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title = "Gabor's signal expansion and a modified Zak transform for a quincunx-type sampling geometry",

abstract = "Gabors signal expansion and the Gabor transform are formulated on a quincunx lattice instead of on the traditional rectangular lattice; the representation of the quincunx lattice is based on the rectangular lattice via either a shear operation or a rotation operation. A modified Zak transformation is defined with the help of which Gabor's signal expansion and the Gabor transform can be brought into product forms that are identical to the ones that are well known for the rectangular sampling geometry. The shear operation on the lattice is associated with an operation on the synthesis and the analysis window, consisting of a multiplication by a quadratic-phase function. Following this procedure, the well-known biorthogonality condition for the window functions in the rectangular sampling geometry can be directly translated to the quincunx case.",

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booktitle = "Proc. ISSPA '99, Fifth International Symposium on Signal Processing and its Applications, Brisbane, Australia",

publisher = "Queensland University of Technology",

note = "ISSPA '99, Fifth International Symposium on Signal Processing and its Applications ; Conference date: 22-08-1999 Through 25-08-1999",

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Bastiaans, MJ & Leest, van, AJ 1999, Gabor's signal expansion and a modified Zak transform for a quincunx-type sampling geometry. in M Deriche, B Boashash & WW Boles (eds), Proc. ISSPA '99, Fifth International Symposium on Signal Processing and its Applications, Brisbane, Australia. Queensland University of Technology, Brisbane, QLD, Australia, pp. 259-262, ISSPA '99, Fifth International Symposium on Signal Processing and its Applications, Brisbane, Australia, 22/08/99. https://doi.org/10.1109/ISSPA.1999.818162

Gabor's signal expansion and a modified Zak transform for a quincunx-type sampling geometry. / Bastiaans, M.J.; Leest, van, A.J.

Proc. ISSPA '99, Fifth International Symposium on Signal Processing and its Applications, Brisbane, Australia. ed. / M. Deriche; B. Boashash; W.W. Boles. Brisbane, QLD, Australia : Queensland University of Technology, 1999. p. 259-262.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AB - Gabors signal expansion and the Gabor transform are formulated on a quincunx lattice instead of on the traditional rectangular lattice; the representation of the quincunx lattice is based on the rectangular lattice via either a shear operation or a rotation operation. A modified Zak transformation is defined with the help of which Gabor's signal expansion and the Gabor transform can be brought into product forms that are identical to the ones that are well known for the rectangular sampling geometry. The shear operation on the lattice is associated with an operation on the synthesis and the analysis window, consisting of a multiplication by a quadratic-phase function. Following this procedure, the well-known biorthogonality condition for the window functions in the rectangular sampling geometry can be directly translated to the quincunx case.

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Bastiaans MJ, Leest, van AJ. Gabor's signal expansion and a modified Zak transform for a quincunx-type sampling geometry. In Deriche M, Boashash B, Boles WW, editors, Proc. ISSPA '99, Fifth International Symposium on Signal Processing and its Applications, Brisbane, Australia. Brisbane, QLD, Australia: Queensland University of Technology. 1999. p. 259-262 https://doi.org/10.1109/ISSPA.1999.818162