Abstract
Time-frequency analysis plays a central role in signal analysis, because signals that have highly concentrated time-frequency content are used in many applications. The uncertainty principle in Fourier analysis sets a limit to the possible simultaneous concentration of a function and its Dunkl transform. To localize signals in the time-frequency plane we use time-frequency localization operators in the Dunkl setting to measure their time-frequency content on some subset of finite measure. Then, using eigenfunctions of these operators, which are maximally time-frequency concentrated, we prove a characterization of functions that are time-frequency concentrated in the region of interest, and we obtain approximation inequalities for such functions using a finite linear combination of eigenfunctions.