Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals

作者：Tropp Joel A^*; Laska Jason N; Duarte Marco F; Romberg Justin K; Baraniuk Richard G

来源：IEEE Transactions on Information Theory, 2010, 56(1): 520-544.

DOI：10.1109/TIT.2009.2034811

• Analog-to-digital conversion
• compressive sampling
• sampling theory
• signal recovery
• sparse approximation

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.

• 出版日期2010-1