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In my talk I will consider two topics that play an important role in digital signal processing: (i) Signal reconstruction and (ii) Time-Frequency analysis based on Weyl-Heisenberg systems.

In the first part of my talk I give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform s ampling from a numerical analysis view point. Among others it is shown how the choice of the finite-dimensional model determines the efficiency and robustness of the resulting numerical al gorithms.In the one approach (often proposed in the literature) the finite-dimensional model leads to an ill-posed problem even in very simple situations. The other model that we consider leads to a well-posed problem that preserves important structural properties of the original infinite-dimensional problem and gives rise to efficient numerical algorithms.

In the second part of the talk I will focus on Weyl-Heisenberg (Gabor) systems. A Weyl-Heisenberg system is generated from a single function by translations and modulations. These systems play for instance a crucial role in modern communication systems. I will address some some numerical aspects of Weyl-Heisenberg systems.