From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

10 Nov 2009 | Moshe Mishali, Student Member, IEEE, and Yonina C. Eldar, Senior Member, IEEE
This paper addresses the challenging problem of blind sub-Nyquist sampling of multiband signals, where the frequency support occupies only a small portion of a wide spectrum. The authors propose a system called the Modulated Wideband Converter (MWC), which multiplies the analog signal by a bank of periodic waveforms, followed by lowpass filtering and uniform sampling at a low rate. Perfect recovery is achieved under certain conditions. The paper also develops a digital architecture for reconstructing the analog input or processing any band of interest at a low rate without interpolating to the Nyquist rate. Numerical simulations demonstrate robustness to noise and mismodeling, potential hardware simplifications, real-time performance for time-varying signals, and stability to quantization effects. The MWC is compared with two previous approaches: periodic nonuniform sampling and the random demodulator, showing its advantages in terms of bandwidth, computational load, and practical implementation. The main contributions include the MWC system and a digital architecture for low-rate processing and recovery, with extensive numerical evaluations supporting the theoretical findings.This paper addresses the challenging problem of blind sub-Nyquist sampling of multiband signals, where the frequency support occupies only a small portion of a wide spectrum. The authors propose a system called the Modulated Wideband Converter (MWC), which multiplies the analog signal by a bank of periodic waveforms, followed by lowpass filtering and uniform sampling at a low rate. Perfect recovery is achieved under certain conditions. The paper also develops a digital architecture for reconstructing the analog input or processing any band of interest at a low rate without interpolating to the Nyquist rate. Numerical simulations demonstrate robustness to noise and mismodeling, potential hardware simplifications, real-time performance for time-varying signals, and stability to quantization effects. The MWC is compared with two previous approaches: periodic nonuniform sampling and the random demodulator, showing its advantages in terms of bandwidth, computational load, and practical implementation. The main contributions include the MWC system and a digital architecture for low-rate processing and recovery, with extensive numerical evaluations supporting the theoretical findings.
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