Sampling of pulse streams: Achieving the rate of innovation

We consider the problem of sampling signals which are comprised of pulse streams. This model belongs to the recently introduced framework of signals with finite rate of innovation. The minimal sampling rate for such signals is the number of degrees of freedom per unit of time, referred to as the rate of innovation. Although sampling of pulse streams was treated in various works, either the rate of innovation was not achieved, or the pulse shape was limited to diracs. In this work we propose multichannel schemes for arbitrary pulse streams, operating at the rate of innovation. The proposed approach is based on modulating the input signal in each channel with a properly chosen waveform, followed by an integrator. We show that the pulses delays and amplitudes can be recovered from the samples using standard spectral estimation tools. The resulting scheme is flexible and exhibits better noise robustness than previous approaches.