1. Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals.
- Author
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Tropp, Joel A., Laska, Jason N., Duarte, Marco F., Romberg, Justin K., and Baraniuk, Richard G.
- Subjects
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DIGITIZATION , *SIGNAL processing , *INFORMATION measurement , *BROADBAND communication systems , *CONVEX programming - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2010
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