Super-resolution of periodic signals from short sequences of samples

TL;DR

This paper introduces a new super-resolution algorithm for reconstructing undersampled periodic signals from short, noisy sample sequences without prior knowledge of the period or bandlimitedness, validated with real data.

Contribution

A novel algorithm that reconstructs periodic signals from short, noisy samples without requiring bandlimitedness or noiseless data, advancing signal processing capabilities.

Findings

Effective reconstruction from short, noisy sequences

Does not require prior period knowledge

Validated with real-world data

Abstract

Reconstruction of undersampled periodic signals of unknown period is an important signal processing operation. It is especially difficult operation when the sequences of samples are short and no information on the inter-sequence time distances is given. For such a case, there exist some algorithms that allow for approximation of the sampled signal. However, these algorithms require either bandlimitedness of the signal, or noiseless samples. In this paper, we propose a novel algorithm which does not require the signal to be bandlimited and it can cope with additive noise in the samples. The algorithm is illustrated and validated with real data.