The Weizmann Institute of Science
Faculty of Mathematics and Computer Science
Vision and Robotics Seminar
Nir Sochen
Tel-Aviv University
will speak on
Group Representation Approach to Digital Signal Processing
Abstract:
Various interesting problems in different fields of digital signal processing
share the same properties. In particular radar signal design, CDMA and sparsity
are all of need of signals with marked properties. Whether such signals exist
and if yes how to construct them were open questions until recently.
I will present in this talk a unified approach that answer these questions. For
that sake I will introduce tools from group representation theory that are
instrumental in the construction of the desired signals.
After presenting the basic objects and tools from representation theory I
proceed by recasting many known results in signal processing via the group of
time and frequency shifts i.e. the Heisenberg group. I show that the Heisenberg
group representation theory is a proper tool for presenting various bases for
the Hilbert space of signals and demonstrate that the fractional Fourier
transform is a direct consequence of the Stone von-Neumann theorem.
I then follow by presenting the less known Weil representation. This is a
group of operators that acts on the time-frequency plane. I show that the tools
that were presented in the treatment of the Heisenberg group can be applied in
this case as well. This results in a novel construction: The ``Oscillator
system" of signals. I will discuss the construction and properties of this new
system.
Joint work with Shamgar Gurevich and Ronny Hadani.
The lecture will take place in the
Lecture Hall, Room 1, Ziskind Building
on Thursday, March 6, 2008
12:00 - 13:00