Sub-Nyquist sampling of short pulses

—We develop sub-Nyquist sampling systems for analog signals comprised of several, possibly overlapping, finite duration pulses with unknown shapes and time positions. Efficient sampling schemes when either the pulse shape or the locations of the pulses are known have been previously developed. To the best of our knowledge, stable and low-rate sampling strategies for continuous signals that are superpositions of unknown pulses without knowledge of the pulse locations have not been derived. The goal in this paper is to fill this gap. We propose a multichannel scheme based on Gabor frames that exploits the sparsity of signals in time and enables sampling multipulse signals at subNyquist rates. Our approach is based on modulating the input signal in each channel with a properly chosen waveform, followed by an integrator. We show that, with proper preprocessing, the Gabor coefficients necessary for almost perfect reconstruct of the input signal, can be recovered from the samples using...

• Type: Journal
• Year: 2011
• Where: ICASSP
• Authors: Ewa Matusiak, Yonina C. Eldar
• Keywords: Efficient Sampling Schemes, ICASSP 2011, Input Signal, Pulses, Signal Processing