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

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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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.

Originele taal-2	Engels
Titel	Proc. ISSPA '99, Fifth International Symposium on Signal Processing and its Applications, Brisbane, Australia
Redacteuren	M. Deriche, B. Boashash, W.W. Boles
Plaats van productie	Brisbane, QLD, Australia
Uitgeverij	Queensland University of Technology
Pagina's	259-262
ISBN van geprinte versie	1 86435 451 8
DOI's	https://doi.org/10.1109/ISSPA.1999.818162
Status	Gepubliceerd - 1999
Evenement	ISSPA '99, Fifth International Symposium on Signal Processing and its Applications - Brisbane, Australië Duur: 22 aug. 1999 → 25 aug. 1999

Congres

Congres	ISSPA '99, Fifth International Symposium on Signal Processing and its Applications
Land/Regio	Australië
Stad	Brisbane
Periode	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 (editors), Proc. ISSPA '99, Fifth International Symposium on Signal Processing and its Applications, Brisbane, Australia (blz. 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. redacteur / M. Deriche ; B. Boashash ; W.W. Boles. Brisbane, QLD, Australia : Queensland University of Technology, 1999. blz. 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.",

author = "M.J. Bastiaans and \{Leest, van\}, A.J.",

year = "1999",

doi = "10.1109/ISSPA.1999.818162",

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

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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N2 - 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.

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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M3 - Conference contribution

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BT - Proc. ISSPA '99, Fifth International Symposium on Signal Processing and its Applications, Brisbane, Australia

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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, redacteurs, Proc. ISSPA '99, Fifth International Symposium on Signal Processing and its Applications, Brisbane, Australia. Brisbane, QLD, Australia: Queensland University of Technology. 1999. blz. 259-262 doi: 10.1109/ISSPA.1999.818162

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

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