Xampling: Analog-to-digital at Sub-Nyquist rates

February 25, 2010 @ 12:00pm Room 1065 Kemper
Dr. Yonina C. Eldar
Massachusetts Institute of Technology (MIT), Cambridge

Abstract:

Signal processing methods have changed substantially over the last several decades. The number of operations that are shifted from analog to digital is constantly increasing. While technology advances enable mass processing of huge data streams, the acquisition capabilities do not scale sufficiently fast so that the conversion to digital has become a serious bottleneck. For some applications, the maximal frequency of the input signals, which dictates the Nyquist rate, already exceeds the possible rates achievable with existing devices.

In this talk, we present a new framework for sampling wideband analog signals at rates far below that dictated by the Nyquist rate. We refer to this methodology as Xampling: A combination of compression and sampling, performed simultaneously. Xampling merges results from standard sampling theory with recent developments in the field of compressed sensing in order to directly sample a wide class of analog signals at very low rates using existing hardware devices. This paradigm relies on exploiting structure inherent to many different classes of signals, which can be modeled mathematically as a union of subspaces.

We begin by introducing the Xampling methodology and explaining why both sampling and compressed sensing alone are insufficient to address low rate sampling of a wide variety of analog signals. We then consider some specific examples including low rate sampling of multiband signals and recovery of time delays from low rate samples.

Bio:

Dr. Yonina C. Eldar Yonina C. Eldar received the B.Sc. degree in Physics in 1995 and the B.Sc. degree in Electrical Engineering in 1996 both from Tel-Aviv University (TAU), Tel-Aviv, Israel, and the Ph.D. degree in Electrical Engineering and Computer Science in 2001 from the Massachusetts Institute of Technology (MIT), Cambridge.

From January 2002 to July 2002 she was a Postdoctoral Fellow at the Digital Signal Processing Group at MIT. She is currently a Professor in the Department of Electrical Engineering at the Technion - Israel Institute of Technology, Haifa, Israel. She is also a Research Affiliate with the Research Laboratory of Electronics at MIT.

Dr. Eldar was in the program for outstanding students at TAU from 1992 to 1996. In 1998, she held the Rosenblith Fellowship for study in Electrical Engineering at MIT, and in 2000, she held an IBM Research Fellowship. From 2002-2005 she was a Horev Fellow of the Leaders in Science and Technology program at the Technion and an Alon Fellow. In 2004, she was awarded the Wolf Foundation Krill Prize for Excellence in Scientific Research, in 2005 the Andre and Bella Meyer Lectureship, in 2007 the Henry Taub Prize for Excellence in Research, in 2008 the Hershel Rich Innovation Award, the Award for Women with Distinguished Contributions, the Muriel & David Jacknow Award for Excellence in Teaching, and the Technion Outstanding Lecture Award, and in 2009 the Technion's Award for Excellence in Teaching. She is a member of the IEEE Signal Processing Theory and Methods technical committee and the Bio Imaging Signal Processing technical committee, an Associate Editor for the IEEE Transactions on Signal Processing, the EURASIP Journal of Signal Processing, the SIAM Journal on Matrix Analysis and Applications, and the SIAM Journal on Imaging Sciences, and on the Editorial Board of Foundations and Trends in Signal Processing.