2011 Poster Sessions : Discrete Sampling in Bandlimited Spaces

Student Name : Aditya Siripuram
Advisor : Brad Osgood
Research Areas: Information Systems
Abstract:
Nyquist Shannon Sampling can be very inefficient for a bandlimited signal without any structure in its support. In this work, we attempt to generalize the Nyquist Shannon sampling theorem to finite dimensional signals with arbitrary frequency support. Assuming we have some knowledge of the frequency support of the signal, we find the locations in which the discrete signal can be sampled without any loss. We investigate conditions on sampling under which the reconstruction process is numerically stable. In particular, when we force the reconstruction system to be orthogonal, we observe interesting connections to the tiling problem in Combinatorics. These ideas of discrete sampling can be extended to arbitrary subspaces.

Our scheme is in contrast to contemporary schemes like compressed sensing which assume that linear combinations of the signal can be observed: in this work we assume that only samples of the signal can be observed.

Bio:
Aditya Siripuram is a second year PhD student in Electrical Engineering Department of Stanford University advised by Prof Brad Osgood. He received his Bachelor’s degree in Electrical engineering from Indian Institute of Technology, Bombay in 2009. At Stanford, he is a recipient of the Benchmark Stanford Graduate Fellowship. His interests include Signal Processing, Communications, and Algorithms.