Statistical reconstruction of pulse shapes from pulse streams

TL;DR

This paper introduces a statistical method for reconstructing finite-length pulse signals from short sample sequences by analyzing their distribution along a curve in low-dimensional space, ensuring unique signal recovery.

Contribution

It presents a novel approach leveraging the distribution of sample points for pulse reconstruction, with a proven uniqueness guarantee and an algorithm for practical estimation.

Findings

Distribution of sample points uniquely determines the pulse.

Proposed algorithm effectively reconstructs pulse signals.

The method outperforms traditional techniques in accuracy.

Abstract

A short sample sequence of a finite-length pulse signal allows for its reconstruction only if the signal has a sparse representation in some basis. The recurrence of the pulse allows for a statistical approach to its reconstruction. We propose a novel method for this task. It is based on the distribution of short sample sequences treated as points which lie along a curve in a low-dimensional Euclidean space. We prove that the probability distribution of the points along this curve determines the underlying pulse signal uniquely. Based on this discovery, we propose an algorithm for pulse estimation from a finite number of short sequences of pulse-stream samples.