Truncations of generalized shift-invariant systems

Pablo Garcia Alvarez; Ole Christensen; Rae Young Kim

doi:10.4153/S0008439523000929

Truncations of generalized shift-invariant systems

Pablo Garcia Alvarez
, Ole Christensen
, Rae Young Kim

Universidad Nacional de San Luis
Yeungnam University

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

Abstract

We provide conditions under which a generalized shift-invariant (GSI) system can be approximated by a GSI-system for which the generators have compact support in the Fourier domain. The approximation quality will be measured in terms of the Bessel bound (lower frame bound) for the difference between the two GSI-systems. In particular, this leads to easily verifiable conditions for a perturbation of a GSI-system to preserve the frame property.

Original language	English
Journal	Canadian Mathematical Bulletin
Volume	67
Issue number	2
Pages (from-to)	504-515
ISSN	0008-4395
DOIs	https://doi.org/10.4153/S0008439523000929
Publication status	Published - 2024

Keywords

Generalized shift-invariant system
Approximation of generalized shiftinvariant system
Frames

Access to Document

10.4153/S0008439523000929

OpenUrl availability

Check availability in DTU Findit

Cite this

@article{a839691d961d42a7ac8af312f8499ced,

title = "Truncations of generalized shift-invariant systems",

abstract = "We provide conditions under which a generalized shift-invariant (GSI) system can be approximated by a GSI-system for which the generators have compact support in the Fourier domain. The approximation quality will be measured in terms of the Bessel bound (lower frame bound) for the difference between the two GSI-systems. In particular, this leads to easily verifiable conditions for a perturbation of a GSI-system to preserve the frame property.",

keywords = "Generalized shift-invariant system, Approximation of generalized shiftinvariant system, Frames",

author = "Alvarez, \{Pablo Garcia\} and Ole Christensen and Kim, \{Rae Young\}",

year = "2024",

doi = "10.4153/S0008439523000929",

language = "English",

volume = "67",

pages = "504--515",

journal = "Canadian Mathematical Bulletin",

issn = "0008-4395",

publisher = "Canadian Mathematical Society",

number = "2",

}

TY - JOUR

T1 - Truncations of generalized shift-invariant systems

AU - Alvarez, Pablo Garcia

AU - Christensen, Ole

AU - Kim, Rae Young

PY - 2024

Y1 - 2024

N2 - We provide conditions under which a generalized shift-invariant (GSI) system can be approximated by a GSI-system for which the generators have compact support in the Fourier domain. The approximation quality will be measured in terms of the Bessel bound (lower frame bound) for the difference between the two GSI-systems. In particular, this leads to easily verifiable conditions for a perturbation of a GSI-system to preserve the frame property.

AB - We provide conditions under which a generalized shift-invariant (GSI) system can be approximated by a GSI-system for which the generators have compact support in the Fourier domain. The approximation quality will be measured in terms of the Bessel bound (lower frame bound) for the difference between the two GSI-systems. In particular, this leads to easily verifiable conditions for a perturbation of a GSI-system to preserve the frame property.

KW - Generalized shift-invariant system

KW - Approximation of generalized shiftinvariant system

KW - Frames

U2 - 10.4153/S0008439523000929

DO - 10.4153/S0008439523000929

M3 - Journal article

SN - 0008-4395

VL - 67

SP - 504

EP - 515

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

IS - 2

ER -

Truncations of generalized shift-invariant systems

Abstract

Keywords

Access to Document

OpenUrl availability

Fingerprint

Cite this