**ABSTRACT**
### Uncertainty Principles for Time-Frequency
Representations

#### K. Gröchenig

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Department of Mathematics, The University of Connecticut, Storrs, CT 06269-3009, USA

We present a machine to produce new uncertainty principles from old ones. Traditionally
an uncertainty principle is an inequality involving both a function $f$ and its Fourier transform
$\hat{f} $. To generate new uncertainty principles, we interpret the pair $(f, \hat{f} )$
as a time-frequency representation, replace it by a different time-frequency representation, and formulate a
corresponding inequality. We discuss a few recent uncertainty principles
for the short-time Fourier transform and the Wigner distribution that can be obtained in this way and
suggest further problems.