Abstract
Window design is a central problem in time-frequency analysis. We have seen in Chapter 12.2 that the quality of the window is crucial for a quantitative description of time-frequency concentration. Technically, the analysis of a decay order of v(x, ω)−1 in the time-frequency plane requires a pair of dual windows g and γ in M 1v . While it is easy to design a window g ∈ M 1 v the quality of the dual window is related to the invertibility of the Gabor frame operator on My (Proposition 12.2.7) and so needs further analysis.
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© 2001 Springer Science+Business Media New York
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Gröchenig, K. (2001). Window Design and Wiener’s Lemma. In: Foundations of Time-Frequency Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0003-1_14
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DOI: https://doi.org/10.1007/978-1-4612-0003-1_14
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6568-9
Online ISBN: 978-1-4612-0003-1
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