## Pairs of dual periodic frames

Publication: Research - peer-review › Journal article – Annual report year: 2012

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**Pairs of dual periodic frames.** / Christensen, Ole; Goh, Say Song.

Publication: Research - peer-review › Journal article – Annual report year: 2012

### Harvard

*Applied and Computational Harmonic Analysis*, vol 33, no. 3, pp. 315-329. DOI: 10.1016/j.acha.2011.12.003

### APA

*Applied and Computational Harmonic Analysis*,

*33*(3), 315-329. DOI: 10.1016/j.acha.2011.12.003

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### MLA

*Applied and Computational Harmonic Analysis*. 2012, 33(3). 315-329. Available: 10.1016/j.acha.2011.12.003

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### Bibtex

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### RIS

TY - JOUR

T1 - Pairs of dual periodic frames

AU - Christensen,Ole

AU - Goh,Say Song

PY - 2012

Y1 - 2012

N2 - The time–frequency analysis of a signal is often performed via a series expansion arising from well-localized building blocks. Typically, the building blocks are based on frames having either Gabor or wavelet structure. In order to calculate the coefficients in the series expansion, a dual frame is needed. The purpose of the present paper is to provide constructions of dual pairs of frames in the setting of the Hilbert space of periodic functions L2(0,2π). The frames constructed are given explicitly as trigonometric polynomials, which allows for an efficient calculation of the coefficients in the series expansions. The generality of the setup covers periodic frames of various types, including nonstationary wavelet systems, Gabor systems and certain hybrids of them.

AB - The time–frequency analysis of a signal is often performed via a series expansion arising from well-localized building blocks. Typically, the building blocks are based on frames having either Gabor or wavelet structure. In order to calculate the coefficients in the series expansion, a dual frame is needed. The purpose of the present paper is to provide constructions of dual pairs of frames in the setting of the Hilbert space of periodic functions L2(0,2π). The frames constructed are given explicitly as trigonometric polynomials, which allows for an efficient calculation of the coefficients in the series expansions. The generality of the setup covers periodic frames of various types, including nonstationary wavelet systems, Gabor systems and certain hybrids of them.

KW - Periodic frames

KW - Gabor frames

KW - Wavelet frames

KW - Dual pairs of frames

KW - Trigonometric polynomials

U2 - 10.1016/j.acha.2011.12.003

DO - 10.1016/j.acha.2011.12.003

M3 - Journal article

VL - 33

SP - 315

EP - 329

JO - Applied and Computational Harmonic Analysis

T2 - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

SN - 1063-5203

IS - 3

ER -