Reconstruction of Signals From Level-Crossing Samples Using Implicit Information

This paper focuses on the recovery of bandlimited signals from level-crossing samples by exploiting not only the knowledge of when given levels are crossed by the input, but also the implicit information that the signal stays between neighboring levels in the time intervals between the level crossings. We propose to use the technique of projection onto convex sets (POCS) for perfect signal reconstruction from either the level crossings or the associated implicit information. Two POCS algorithms are proposed: iterative POCS and one-step POCS. While the one-step POCS is based on matrix inversion, the iterative projections can be implemented using a chain of standard circuit operations: a low-pass filter and a clipping circuit, respectively. The perfect signal recovery of the infinite projection iteration can be viewed as the completion of the nonperfect input reconstruction achieved in continuous-time digital signal processing from level crossings. The comparative analysis of simulation results for both iterative and one-step POCS algorithms show the importance of a good selection of the initial guess for the POCS reconstruction.