Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals

By Joel A. Tropp, Jason N. Laska, Marco F. Duarte, Justin K. Romberg, Richard Baraniuk. IEEE Transactions on Information Theory, 2009

1,096 citations recorded by the source corpus.

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.

Subfields: Biomedical Engineering, Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/b8252bc28185c0d8e56aecc803b36b6e92a144db

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Citations in the corpus

Wideband spectrum sensing for cognitive radio networks: a survey (2013, positive): “[11] proposed an analog-to-information converter (AIC), w hich is the basis of the above-mentioned algorithms.”
New and Improved Johnson-Lindenstrauss Embeddings via the Restricted Isometry Property (2010, positive): “This observation has several consequences in the area of compressed sensing, and also allows us to obtain improved JL embedding results for several matrix constructions with existing RIP bounds [13, 35, 31, 38, 33].”
Structured Compressed Sensing: From Theory to Applications (2011, background): “A ﬁrst step in this direction is the architecture known as the random demodulator (RD) [84].”
Compressed Sensing (2014, neutral): “Estas abarcan diversas áreas como: imagenoloǵıa medica [49, 45], conversión analógico/digital [68], detección mediante RADAR [4, 42], corrección de errores [18], cámaras digitales [34, 21, 51], Sismoloǵıa [41], Radioastronomı́a [71], comunicación inalámbrica [63, 3, 65] y redes de sensores inalámbri”
Compressed Synthetic Aperture Radar (2010, background): “The image formation processor produces an image that is a two-dimensional mapping of the illuminated scene [4].”
Compressive Sensing with structured random matrices (2012, background): “Although we will not cover specific applications in these notes, let us mention that compressive sensing may be applied in imaging [44, 109], A/D conversion [133], radar [69, 49] and wireless communication [126, 95], to name a few.”
Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors (2011, methodology): “P.B. is funded by Mitsubishi Electric Research Laboratories.”
Compressive Sensing by Random Convolution (2009, methodology): “This fact will be especially important in the imaging architecture discussed in Section 2.2, where measurements are taken by averaging over large pixels.”
Signal Processing With Compressive Measurements (2010, positive): “While theoretical analysis of these matrices remains a topic of active study in the CS community, there do exist guarantees of stable embeddings for such practical architectures [35], [37].”
A Systematic Review of Compressive Sensing: Concepts, Implementations and Applications (2018, background): “Here, φ can be considered as the product of two matrices H and P [18], [19].”
Sparse Recovery Using Sparse Matrices (2010, background): “For examples of compressive sensing hardware, see [13], [31], [41], and [42].”
Xampling: Analog to digital at sub-Nyquist rates (2009, methodology): “The technique of random demodulation underlying [28], [29] was introduced in [30], where the building blocks were simulated in HSPICE for synthetic inputs, matching the discretized model of [28].”
From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals (2009, methodology): “3 and 6, to multicoset sampling [5] and the random demodulator [9], [10].”
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples (2008, positive): “Other types of sampling matrices, such as the random demodulator [35], enjoy similar qualities.”