Sub-Nyquist Sampling of Short Pulses: Part I

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 a superposition of unknown pulses without knowledge of the pulse locations have not been derived. The goal in this two-part 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 sub-Nyquist 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 standard methods of co...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Ewa Matusiak, Yonina C. Eldar
• Keywords: CORR 2010, Education, Efficient Sampling Schemes, Input Signal, Pulses