A Geometric Construction of Tight Multivariate Gabor Frames with Compactly Supported Smooth Windows

Götz E. Pfander; Peter Rashkov; Yang Wang

doi:10.1007/s00041-011-9198-x

A Geometric Construction of Tight Multivariate Gabor Frames with Compactly Supported Smooth Windows

Götz E. Pfander
, Peter Rashkov
, Yang Wang

Research output: Contribution to journal › Journal Article › peer-review

13 Citations (Scopus)

Abstract

Fundamental domains of pairs of lattices were used by Han and Wang to construct multivariate Gabor frames for separable lattices. We build upon their results to obtain Gabor frames with smooth and compactly supported window functions. Our results are applicable, for example, if certain pairs of lattices with equal density allow for a common compact and star-shaped fundamental domain.

Original language	English
Pages (from-to)	223-239
Number of pages	17
Journal	Journal of Fourier Analysis and Applications
Volume	18
Issue number	2
DOIs	https://doi.org/10.1007/s00041-011-9198-x
Publication status	Published - Apr 2012
Externally published	Yes

Keywords

Lattice tilings and packings
Symplectic equivalence
Time-frequency lattices

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10.1007/s00041-011-9198-x

Cite this

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abstract = "Fundamental domains of pairs of lattices were used by Han and Wang to construct multivariate Gabor frames for separable lattices. We build upon their results to obtain Gabor frames with smooth and compactly supported window functions. Our results are applicable, for example, if certain pairs of lattices with equal density allow for a common compact and star-shaped fundamental domain.",

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AU - Pfander, Götz E.

AU - Rashkov, Peter

AU - Wang, Yang

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N2 - Fundamental domains of pairs of lattices were used by Han and Wang to construct multivariate Gabor frames for separable lattices. We build upon their results to obtain Gabor frames with smooth and compactly supported window functions. Our results are applicable, for example, if certain pairs of lattices with equal density allow for a common compact and star-shaped fundamental domain.

AB - Fundamental domains of pairs of lattices were used by Han and Wang to construct multivariate Gabor frames for separable lattices. We build upon their results to obtain Gabor frames with smooth and compactly supported window functions. Our results are applicable, for example, if certain pairs of lattices with equal density allow for a common compact and star-shaped fundamental domain.

KW - Lattice tilings and packings

KW - Symplectic equivalence

KW - Time-frequency lattices

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:000304148700002

UR - https://openalex.org/W1993719646

U2 - 10.1007/s00041-011-9198-x

DO - 10.1007/s00041-011-9198-x

M3 - Journal Article

SN - 1069-5869

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SP - 223

EP - 239

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 2

ER -

A Geometric Construction of Tight Multivariate Gabor Frames with Compactly Supported Smooth Windows

Abstract

Keywords

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