Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals

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 lim...

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Vydané v:	IEEE transactions on information theory Ročník 56; číslo 1; s. 520 - 544
Hlavní autori:	Tropp, J.A., Laska, J.N., Duarte, M.F., Romberg, J.K., Baraniuk, R.G.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York, NY IEEE 01.01.2010 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Analog Analog-digital conversion, digital-analog conversion, pcm coding Analog-to-digital conversion Applied sciences compressive sampling Conversion Data acquisition Demodulation Demodulators Detection, estimation, filtering, equalization, prediction Exact sciences and technology Frequencies Frequency Hardware Information processing Information theory Information, signal and communications theory Mathematical programming Nonlinearity Performance analysis Programming Robustness Sampling Sampling methods Sampling techniques sampling theory Sampling, quantization Signal and communications theory Signal processing signal recovery Signal sampling Signal, noise Simulation sparse approximation Strategy Telecommunications and information theory Wideband Performance evaluation sampling theory Signal sampling compressive sampling AD conversion Analog signal signal recovery Band limited signal Convex programming Data acquisition system AD converter Signal restoration Analog-to-digital conversion Wide band Simulation Sampling rate Signal processing W band A priori estimation sparse approximation Sparse representation Demodulator Signal reconstruction Localization
ISSN:	0018-9448, 1557-9654
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Popis
Shrnutí:	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.
Bibliografia:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 ObjectType-Article-2
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2009.2034811