Sub-Nyquist Sampling Based on Exponential Reproducing Gabor Windows

For analog signals comprised of several, possibly overlapping, finite duration pulses with unknown shapes and time positions, an efficient Sub-Nyquist sampling system is based on Gabor frames. To improve the realizability of this sampling system, we present alternative method for the case that the windows are exponential reproducing Gabor windows. Then, the time translation element could be realized with exponential filters. In this paper, we also construct the measurement matrix and prove that it has better coherence than Fourier matrix. Simulations prove that the sampling proposed in this paper, the sampling system require quite low sampling frequency and has nice reconstruction performance.