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Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals (2009)
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BibTeX
@MISC{Tropp09beyondnyquist:,
author = {Joel A. Tropp and Jason N. Laska and Marco F. Duarte and Justin K. Romberg and Richard G. Baraniuk},
title = { Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals},
year = {2009}
}
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Abstract
Wideband analog signals push contemporary 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 significant frequencies relative to the bandlimit, although the locations of the frequencies may not be known a priori. For this type of sparse signal, other sampling strategies are possible. This paper 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 frequencies in the signal, and let W denote its bandlimit in Hz. Simulations suggest that the random demodulator requires just O(K log(W/K)) samples per second to stably reconstruct the 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. This paper provides a detailed theoretical analysis of the system’s performance that supports the empirical observations.
Keyphrases
sparse bandlimited signal efficient sampling random demodulator nyquist rate total number empirical observation detailed theoretical analysis small number system performance interest contain data acquisition system new type available component performance limit many application convex programming nonlinear method significant frequency sparse signal
