Xampling: Analog-to-digital at Sub Nyquist rates
Yonina C. Eldar, Associate Professor, Department of Electrical Engineering Technion - Israel Institute of Technology
Wednesday, October 28, 2009
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, recovery of time delays from low rate samples, and more generally sampling and recovery over finite and infinite structured unions of subspaces.
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. She is currently an Associate 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.
Professor Eldar 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.