Sub-Nyquist Sampling of Acoustic Signals Based on Chaotic Compressed Sensing

Compressed sensing (CS) is a new approach to signal sampling that allows signal recovery from an incomplete set of samples. For the faithful reconstruction of the signal from few measurements or samples, the sensing matrix must satisfy the restricted isometry property (RIP). The random matrices obey this property, but the practical implementation is expensive. Chaotic sequences are used to construct the sensing matrix and exact reconstruction is, under specific conditions, possible with high probability. In this paper, a chaotic compressive sampler is employed to sample the acoustic signals at sub-Nyquist rate. In contrast with traditional Nyquist sampling and linear reconstruction, orthogonal matching pursuit (OMP) algorithm is applied to recover the signal from the chaotic measurements. This paper shows that the chaotic compressive sampler outperforms the random demodulator architecture in terms of the reconstruction accuracy.