Model space results for the Gabor and wavelet transforms

Gerard Ascensi; Joaquim Bruna

doi:10.1109/TIT.2009.2016028

Model space results for the Gabor and wavelet transforms

Gerard Ascensi, Joaquim Bruna

Departament de Matemàtiques

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Resum

We prove that the unique Gabor window leading to an analytic model space is the Gaussian one, and we give an analogous result for the wavelet transform. For the general case we give a new approach to study irregular Gabor and wavelet frames. We improve some known results for Gabor windows in the Feichtinger algebra, and for a special class of wavelets. © 2009 IEEE.

Idioma original	Anglès
Pàgines (de-a)	2250-2259
Revista	IEEE Transactions on Information Theory
Volum	55
Número	5
DOIs	https://doi.org/10.1109/TIT.2009.2016028
Estat de la publicació	Publicada - 27 de maig 2009

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10.1109/TIT.2009.2016028

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title = "Model space results for the Gabor and wavelet transforms",

abstract = "We prove that the unique Gabor window leading to an analytic model space is the Gaussian one, and we give an analogous result for the wavelet transform. For the general case we give a new approach to study irregular Gabor and wavelet frames. We improve some known results for Gabor windows in the Feichtinger algebra, and for a special class of wavelets. {\textcopyright} 2009 IEEE.",

keywords = "Continuous transform, Frames, Gabor system, Sampling sets, Wavelets",

author = "Gerard Ascensi and Joaquim Bruna",

year = "2009",

month = may,

day = "27",

doi = "10.1109/TIT.2009.2016028",

language = "English",

volume = "55",

pages = "2250--2259",

number = "5",

}

TY - JOUR

T1 - Model space results for the Gabor and wavelet transforms

AU - Ascensi, Gerard

AU - Bruna, Joaquim

PY - 2009/5/27

Y1 - 2009/5/27

N2 - We prove that the unique Gabor window leading to an analytic model space is the Gaussian one, and we give an analogous result for the wavelet transform. For the general case we give a new approach to study irregular Gabor and wavelet frames. We improve some known results for Gabor windows in the Feichtinger algebra, and for a special class of wavelets. © 2009 IEEE.

AB - We prove that the unique Gabor window leading to an analytic model space is the Gaussian one, and we give an analogous result for the wavelet transform. For the general case we give a new approach to study irregular Gabor and wavelet frames. We improve some known results for Gabor windows in the Feichtinger algebra, and for a special class of wavelets. © 2009 IEEE.

KW - Continuous transform

KW - Frames

KW - Gabor system

KW - Sampling sets

KW - Wavelets

U2 - 10.1109/TIT.2009.2016028

DO - 10.1109/TIT.2009.2016028

M3 - Article

SN - 0018-9448

VL - 55

SP - 2250

EP - 2259

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 5

ER -

Model space results for the Gabor and wavelet transforms

Resum

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