Abstract:

I will describe a special class of complex valued functions (digital
signals) on the finite line $\mathbb{F}_{p}$, called the oscillator
functions. These functions satisfy many interesting properties which 
seem to be ideal for applications in various fields of digital signal 
processing, including radar and communication.

I will begin my lecture with a brief exposition of the theory of 
continuos and discrete radar. I will explain why eigenfunctions of 
the harmonic oscillator $D=3D\partial _{t}^{2}-t^{2}$ are ideal 
signals for continuous radar.

My main goal is to describe the oscillator functions as a discrete 
analogue for the eigenfunctions of $D$. In the course, I will introduce 
the Weil representation of the group $SL_{2}$ and hint towards its 
fundamental role in harmonic analysis, both in the continuous and finite 
settings.

Joint work with Shamgar Gurevich (UC Berkeley) and Nir Sochen (Tel Aviv 
University)