Applied Math Seminar
Spring Quarter 2009
SPECIAL: 11:00 a.m.
Sloan Mathematics Corner
SPECIAL: Building 380, Room 380-W

Friday, April 10, 2009

Joel Tropp
Applied and Computational Mathematics
California Institute of Technology

Beyond Nyquist: Efficient sampling of sparse, bandlimited signals


Abstract:

Wideband analog signals routinely push state-of-the-art analog-to-digital conversion systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small number of frequencies relative to the bandwidth. For these type of sparse signals, other sampling strategies are possible.

This talk describes a new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components. Let K denote the total number of significant frequencies, and let W denote the bandwidth in Hz. New theoretical work, supported by empirical studies, establishes that the random demodulator requires just O(K*polylog(W)) samples per second to reconstruct any such signal. This sampling rate is exponentially lower than the Nyquist rate of W Hz. In contrast with Nyquist sampling, one must use nonlinear methods, such as convex programming, to recover the signal from the samples taken by the random demodulator. Rigorous algorithmic guarantees are also available.

Joint with R. Baraniuk, M. Duarte, J. Laska, and J. Romberg.