Beyond Nyquist: Efficient sampling of sparse bandlimited signals

Joel A. Tropp, Jason N. Laska, Marco F. Duarte, Justin K. Romberg, Richard G. Baraniuk

Research output: Contribution to journalArticlepeer-review

922 Scopus citations


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 languageEnglish (US)
Article number5361485
Pages (from-to)520-544
Number of pages25
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - Jan 2010


  • 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


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