Multichannel Sampling of Pulse Streams at the Rate of Innovation

Résumé : We consider minimal-rate sampling schemes for streams of delayed and weighted versions of a known pulse shape. Such signals belong to the class of finite rate of innovation (FRI) models. The minimal sampling rate for these parametric 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 previous works, either the rate of innovation was not achieved, or the pulse shape was limited to diracs and the method was instable for high rates of innovation. In this work we propose a multichannel framework for pulse streams with arbitrary shape, operating at the rate of innovation. Our approach is based on modulating the input signal with a set of properly chosen waveforms, followed by a bank of integrators. We show that the pulse stream can be recovered from the proposed minimal-rate samples using standard tools taken from spectral estimation in a stable way even at high rates of innovation. In addition, we address practical implementation issues, such as reduction of hardware complexity and immunity to failure in the sampling channels. The resulting scheme is flexible and exhibits better noise robustness than previous approaches.