Frames adapted to a phase-space cover

Monika Dörfler; Jose Luis Romero

doi:10.1007/s00365-014-9236-4

Frames adapted to a phase-space cover

Monika Dörfler, Jose Luis Romero

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We construct frames adapted to a given cover of the time-frequency or time-scale plane. The main feature is that we allow for quite general and possibly irregular covers. The frame members are obtained by maximizing their concentration in the respective regions of phase-space. We present applications in time-frequency, wavelet and Gabor analysis.

Original language	English
Pages (from-to)	445 - 484
Number of pages	40
Journal	Constructive Approximation: an international journal for approximations and expansions
Volume	39
Issue number	3
DOIs	https://doi.org/10.1007/s00365-014-9236-4
Publication status	Published - Jun 2014

Austrian Fields of Science 2012

1010 Mathematics

Keywords

Frame
Localization operator
Phase-space
Short-time Fourier transform
Time-frequency analysis
Time-scale analysis

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10.1007/s00365-014-9236-4

Cite this

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title = "Frames adapted to a phase-space cover",

abstract = "We construct frames adapted to a given cover of the time-frequency or time-scale plane. The main feature is that we allow for quite general and possibly irregular covers. The frame members are obtained by maximizing their concentration in the respective regions of phase-space. We present applications in time-frequency, wavelet and Gabor analysis. ",

keywords = "Frame, Localization operator, Phase-space, Short-time Fourier transform, Time-frequency analysis, Time-scale analysis",

author = "Monika D{\"o}rfler and Romero, {Jose Luis}",

note = "Funding Information: Monika D{\"o}rfler was supported by the Austrian Science Fund (FWF): [T384-N13] Locatif and by the WWTF projects Audiominer (MA09-24) and (VRG12-009). Jos{\'e} Luis Romero gratefully acknowledges support from the Austrian Science Fund (FWF): [M1586], [P22746-N13] and [T384-N13].",

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doi = "10.1007/s00365-014-9236-4",

language = "English",

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T1 - Frames adapted to a phase-space cover

AU - Dörfler, Monika

AU - Romero, Jose Luis

N1 - Funding Information: Monika Dörfler was supported by the Austrian Science Fund (FWF): [T384-N13] Locatif and by the WWTF projects Audiominer (MA09-24) and (VRG12-009). José Luis Romero gratefully acknowledges support from the Austrian Science Fund (FWF): [M1586], [P22746-N13] and [T384-N13].

PY - 2014/6

Y1 - 2014/6

N2 - We construct frames adapted to a given cover of the time-frequency or time-scale plane. The main feature is that we allow for quite general and possibly irregular covers. The frame members are obtained by maximizing their concentration in the respective regions of phase-space. We present applications in time-frequency, wavelet and Gabor analysis.

AB - We construct frames adapted to a given cover of the time-frequency or time-scale plane. The main feature is that we allow for quite general and possibly irregular covers. The frame members are obtained by maximizing their concentration in the respective regions of phase-space. We present applications in time-frequency, wavelet and Gabor analysis.

KW - Frame

KW - Localization operator

KW - Phase-space

KW - Short-time Fourier transform

KW - Time-frequency analysis

KW - Time-scale analysis

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U2 - 10.1007/s00365-014-9236-4

DO - 10.1007/s00365-014-9236-4

M3 - Article

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VL - 39

SP - 445

EP - 484

JO - Constructive Approximation: an international journal for approximations and expansions

JF - Constructive Approximation: an international journal for approximations and expansions

IS - 3

ER -

Frames adapted to a phase-space cover

Abstract

Austrian Fields of Science 2012

Keywords

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