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.
In: Applied and Computational Harmonic Analysis, Vol. 33, No. 3, 2012, p. 315-329.Publication: Research - peer-review › Journal article – Annual report year: 2012
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TY - JOUR
T1 - Pairs of dual periodic frames
A1 - Christensen,Ole
A1 - Goh,Say Song
AU - Christensen,Ole
AU - Goh,Say Song
PB - Academic Press
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
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
SN - 1063-5203
IS - 3
VL - 33
SP - 315
EP - 329
ER -