A Topological Lowpass Filter for Quasiperiodic Signals
This addresses the challenge of signal recovery in noisy environments for applications like signal processing, but it appears incremental as it builds on existing topological methods.
The paper tackles the problem of estimating a quasiperiodic function from noisy measurements by introducing a two-stage topological algorithm that first detects the quasiperiodic structure to avoid distortion, resulting in an improved recovery method.
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.