Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605471 | Applied and Computational Harmonic Analysis | 2009 | 6 Pages |
Abstract
We present an example of a complete and minimal Gabor system consisting of time–frequency shifts of a Gaussian, localized at the coordinate axes in the time–frequency plane (phase space). Asymptotically, the number of time–frequency shifts contained in a disk centered at the origin is only 2/π times the number of points from the von Neumann lattice found in the same disk. Requiring a certain regular distribution in phase space, we show that our system has minimal density among all complete and minimal systems of time–frequency shifts of a Gaussian.
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