# Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals

@article{Tropp2010BeyondNE, title={Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals}, author={Joel A. Tropp and Jason N. Laska and Marco F. Duarte and Justin K. Romberg and Richard Baraniuk}, journal={IEEE Transactions on Information Theory}, year={2010}, volume={56}, pages={520-544} }

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…

## 1,015 Citations

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## References

SHOWING 1-10 OF 84 REFERENCES

From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

- Computer ScienceIEEE Journal of Selected Topics in Signal Processing
- 2010

This paper considers the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum, and proposes a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms.

Sampling, data transmission, and the Nyquist rate

- Computer Science
- 1967

It is argued that only stable sampling is meaningful in practice, and it is proved that stable sampling cannot be performed at a rate lower than the Nyquist, and data cannot be transmitted as samples at a Rate of 2W per second, regardless of the location of sampling instants, the nature of the set of frequencies which the signals occupy, or the method of construction.

Analog-to-Information Conversion via Random Demodulation

- Computer Science2006 IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software
- 2006

This paper proposes a system that uses modulation, filtering, and sampling to produce a low-rate set of digital measurements, inspired by the theory of compressive sensing (CS), which states that a discrete signal having a sparse representation in some dictionary can be recovered from a small number of linear projections of that signal.

Efficient sampling of sparse wideband analog signals

- Computer Science2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel
- 2008

This paper proposes an alternative sampling stage that does not require a full-band front end and captures signals with an analog front end that consists of a bank of multipliers and lowpass filters whose cutoff is much lower than the Nyquist rate.

Compressed Sensing of Analog Signals

- Computer ScienceArXiv
- 2008

A general framework for sampling of analog-signals for which no underly ing finite-dimensional model exists is developed and allows to extend much of the recent literature on CS to the truly analog domain.

Blind Multiband Signal Reconstruction: Compressed Sensing for Analog Signals

- Computer Science, MathematicsIEEE Transactions on Signal Processing
- 2009

This paper describes how to choose the parameters of the multi-coset sampling so that a unique multiband signal matches the given samples, and develops a theoretical lower bound on the average sampling rate required for blind signal reconstruction, which is twice the minimal rate of known-spectrum recovery.

Compressed Sensing of Analog Signals in Shift-Invariant Spaces

- Computer ScienceIEEE Transactions on Signal Processing
- 2009

This paper develops methods for low-rate sampling of continuous-time sparse signals in shift-invariant (SI) spaces, generated by m kernels with period T .

Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon Meets Strang–Fix

- Computer ScienceIEEE Transactions on Signal Processing
- 2007

This paper shows that many signals with a finite rate of innovation can be sampled and perfectly reconstructed using physically realizable kernels of compact support and a local reconstruction algorithm.

Random Sampling for Analog-to-Information Conversion of Wideband Signals

- Computer Science2006 IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software
- 2006

A framework for analog-to-information conversion that enables sub-Nyquist acquisition and processing of wideband signals that are sparse in a local Fourier representation is developed and an efficient information recovery algorithm is developed to compute the spectrogram of the signal, which is dubbed the sparsogram.

Toeplitz Compressed Sensing Matrices With Applications to Sparse Channel Estimation

- Computer ScienceIEEE Transactions on Information Theory
- 2010

It is shown here that time-domain probing of a multipath channel with a random binary sequence, along with utilization of CS reconstruction techniques, can provide significant improvements in estimation accuracy compared to traditional least-squares based linear channel estimation strategies.