Beyond Nyquist: efficient sampling of sparse bandlimited signals

Wideband analog signals push contemporary analog-to-digital conversion 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 bandlimit, 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 bandlimit in Hz. Simulations show 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 Hz. In contrast with Nyquist sampling, one must use nonlinear methods, such as convex programming, to recover the si...

• Type: Journal
• Year: 2010
• Where: TIT
• Authors: Joel A. Tropp, Jason N. Laska, Marco F. Duarte, Justin K. Romberg, Richard G. Baraniuk
• Keywords: Contemporary Analog-to-digital Conversion, Education, Nyquist Rate, Random Demodulator, TIT 2010