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- W1521307103 abstract "Short-time Fourier analysis, an unavoidable tool in signal processing, is easily formulated with the use of time-frequency atoms. Depending on the form and length of the analysis window, it allows the localization of transient phenomena and the estimation of instantaneous frequencies, but the Heisenberg uncertainty principle imposes a compromise between these two uses. Weyl-Heisenberg frames studied within the framework of Gabor analysis decrease the intrinsic redundancy of the short-time Fourier transform. However, it is impossible to obtain in this manner an orthonormal basis of localized time-frequency atoms: this is the Balian-Low theorem, which can be bypassed by Wilson bases and frames. Conversely, extremely redundant multi-scale dictionaries of time-frequency atoms are used in conjunction with adaptive decompositions in order to bypass the uncertainty principle." @default.
- W1521307103 created "2016-06-24" @default.
- W1521307103 creator A5041230403 @default.
- W1521307103 date "2008-01-01" @default.
- W1521307103 modified "2023-09-23" @default.
- W1521307103 title "Linear Time-Frequency Analysis I: Fourier-Type Representations" @default.
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- W1521307103 doi "https://doi.org/10.1002/9780470611203.ch3" @default.
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