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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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 56; no. 1; pp. 520 - 544
Main Authors: Tropp, J.A., Laska, J.N., Duarte, M.F., Romberg, J.K., Baraniuk, R.G.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.01.2010
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Description
Summary: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.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2009.2034811