Abstract
Wavelet (or continuous wavelet) transform is superior to the Fourier transform and the windowed (or short-time Fourier) transform because of its ability to measure the time–frequency variations in a signal at different time–frequency resolutions. However, the uncertainty principles in Fourier analysis set a limit to the maximal time–frequency resolution. We present some forms of uncertainty principles for functions that are \(\varepsilon \)-concentrated in a given region within the time–frequency plane involving particularly localization operators. Moreover we show how the eigenfunctions of such localization operators are maximally time–frequency-concentrated in the region of interest and we will use it to approximate such \(\varepsilon \)-concentrated functions.
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Ghobber, S. Localization measures in the time-scale setting. J. Pseudo-Differ. Oper. Appl. 8, 389–410 (2017). https://doi.org/10.1007/s11868-017-0195-y
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DOI: https://doi.org/10.1007/s11868-017-0195-y