## 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.

Original language | English (US) |
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Article number | 5361485 |

Pages (from-to) | 520-544 |

Number of pages | 25 |

Journal | IEEE Transactions on Information Theory |

Volume | 56 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2010 |

## Keywords

- Analog-to-digital conversion
- Compressive sampling
- Sampling theory
- Signal recovery
- Sparse approximation

## ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences