Sampling and sparsity: from vectors and functions to matrices and operators
given at strobl07 (20.06.07 09:30)
We outline the identification problem for matrices and operators with "sparse representations" and show how this leads to a generalization of Shannon's sampling theorem and of the identifiability of time invariant operators to larger classes of pseudodifferential operators of any degree. In this overview talk we discuss operators with discretly supported spreading functions (Gabor frame operators), compactly supported spreading function (underspread operators) and bandlimited or compactly supported Weyl symbols.
We give applications to
- wireless communication channels
- multiple-input multiple-output channels