Reconstruction of Recurring Pulses From Distribution of Short Sequences of Samples

Abstract

To accurately reconstruct a finite-length pulse signal from a short sequence of non-zero samples, the signal must have a sparse representation in a specific basis. However, if the pulse recurs in time, a statistical approach can be employed for its reconstruction. In this study, we introduce a novel method for this purpose. Our method is based on analyzing the distribution of short sample sequences as points along an open curve in a low-dimensional Euclidean space. We demonstrate that the probability distribution of these points uniquely determines the original pulse signal. Leveraging this finding, we propose an algorithm that estimates the pulse signal using a finite number of short sequences of samples derived from a pulse-stream signal. The correctness of the proposed algorithm is confirmed through numerical experiments, which we present in this study.