Dunkl-Gabor transform and time-frequency concentration
The aim of this paper is to prove two new uncertainty principles for the Dunkl-Gabor transform. The first of these results is a new version of Heisenberg’s uncertainty inequality which states that the Dunkl-Gabor transform of a nonzero function with respect to a nonzero radial window function cannot be time and frequency concentrated around zero. The second result is an analogue of Benedicks’ uncertainty principle which states that the Dunkl-Gabor transform of a nonzero function with respect to a particular window function cannot be time-frequency concentrated in a subset of the form S × B(0, b) in the time-frequency plane ℝ d × ℝ̂ d . As a side result we generalize a related result of Donoho and Stark on stable recovery of a signal which has been truncated and corrupted by noise.
Keywordstime-frequency concentration Dunkl-Gabor transform uncertainty principles
MSC 201042C20 43A32 46E22
Unable to display preview. Download preview PDF.
- J. A. Hogan, J. D. Lakey: Time-Frequency and Time-Scale Methods: Adaptive Decompositions, Uncertainty Principles, and Sampling. Applied and Numerical Harmonic Analysis, Birkhäuser, Boston, 2005.Google Scholar