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Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals

Tropp, Joel A. and Laska, Jason N. and Duarte, Marco F. and Romberg, Justin K. and Baraniuk, Richard G. (2010) Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals. IEEE Transactions on Information Theory, 56 (1). pp. 520-544. ISSN 0018-9448. https://resolver.caltech.edu/CaltechAUTHORS:20100119-103356110

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Abstract

Wideband analog signals push contemporary analog- to-digital conversion (ADC) 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 band limit, 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 band limit in hertz. 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 $W$ hertz. In contrast to 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/TIT.2009.2034811DOIArticle
http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=5361485PublisherArticle
https://arxiv.org/abs/0902.0026arXivDiscussion Paper
ORCID:
AuthorORCID
Tropp, Joel A.0000-0003-1024-1791
Baraniuk, Richard G.0000-0002-0721-8999
Additional Information:© 2010 IEEE. Current Version Published [online]: 2009-12-28. Manuscript received January 31, 2009; revised September 18, 2009. Current version published December 23, 2009. The work of J. A. Tropp was supported by ONR under Grant N00014-08-1-0883, DARPA/ONR under Grants N66001-06-1-2011 and N66001-08-1-2065, and NSF under Grant DMS-0503299. The work of J. N. Laska, M. F. Duarte, and R. G. Baraniuk was supported by DARPA/ONR under Grants N66001-06-1-2011 and N66001-08-1-2065, ONR under Grant N00014-07-1-0936, AFOSR under Grant FA9550-04-1-0148, NSF under Grant CCF-0431150, and the Texas Instruments Leadership University Program. The work of J. K. Romberg was supported by NSF under Grant CCF-515632. The material in this paper was presented in part at SampTA 2007, Thessaloniki, Greece, June 2007.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-08-1-0883
Office of Naval Research (ONR)N66001-06-1-2011
Office of Naval Research (ONR)N66001-08-1-2065
NSFDMS-0503299
Office of Naval Research (ONR)N00014-07-1-0936
Air Force Office of Scientific Research (AFOSR)FA9550-04-1-0148
NSFCCF-0431150
Texas InstrumentsUNSPECIFIED
NSFCCF-515632
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Subject Keywords:Analog-to-digital conversion; compressive sampling; sampling theory; signal recovery; sparse approximation
Issue or Number:1
Record Number:CaltechAUTHORS:20100119-103356110
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20100119-103356110
Official Citation:Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals Tropp, J. A.; Laska, J. N.; Duarte, M. F.; Romberg, J. K.; Baraniuk, R. G.; Information Theory, IEEE Transactions on Volume 56, Issue 1, Jan. 2010 Page(s):520 - 544
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17210
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:25 Jan 2010 19:29
Last Modified:03 Oct 2019 01:24

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