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 $$\varepsilon $$ ε -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 $$\varepsilon $$ ε -concentrated functions.
Journal of Pseudo-Differential Operators and Applications – Springer Journals
Published: Mar 1, 2017
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