A Topological Lowpass Filter for Quasiperiodic Signals

TL;DR

This paper introduces a topological lowpass filter that accurately recovers quasiperiodic signals from noisy data by estimating phase without distortion, even with many samples.

Contribution

It proposes a novel two-stage topological algorithm for quasiperiodic signal recovery that preserves signal integrity without restrictive assumptions.

Findings

Effective noise reduction in quasiperiodic signals

Accurate phase estimation without distortion

Robust performance with large sample sizes

Abstract

This article presents a two-stage topological algorithm for recovering an estimate of a quasiperiodic function from a set of noisy measurements. The first stage of the algorithm is a topological phase estimator, which detects the quasiperiodic structure of the function without placing additional restrictions on the function. By respecting this phase estimate, the algorithm avoids creating distortion even when it uses a large number of samples for the estimate of the function.