In the lecture we will explain how various fundamental structures from group representation theory appear naturally in the context of discrete harmonic analysis and can be applied to solve concrete problems from
digital signal processing. We will begin the lecture by describing our solution
to the problem of Â…finding a canonical orthonormal basis of eigenfunctions of the
discrete Fourier transform (DFT). Then we will explain how to generalize the
construction to obtain a larger collection of functions that we call “The oscillator dictionary”. Functions in the oscillator dictionary admit many interesting
properties, in particular, we will explain several of these properties which arise
in the context of problems of current interest in areas such as communication
and radar.
Joint work with Nir Sochen (Tel Aviv).