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 epsilon-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 epsilon-concentrated functions.