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

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

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10.4153/S0008439523000929

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

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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

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DO - 10.4153/S0008439523000929

M3 - Journal article

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VL - 67

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JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

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Truncations of generalized shift-invariant systems

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Keywords

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