Robust Zero-crossings Detection in Noisy Signals using Topological Signal Processing

TL;DR

This paper introduces a topological data analysis method using persistent homology for robust zero-crossings detection in noisy signals, outperforming existing techniques in accuracy and speed.

Contribution

The authors develop a novel TDA-based algorithm for zero-crossings detection that is robust to noise and provides comprehensive root bracketing, with automatic threshold setting.

Findings

Faster convergence compared to software-based methods

Higher accuracy in zero-crossings detection

Capable of finding all roots within an interval

Abstract

We explore a novel application of zero-dimensional persistent homology from Topological Data Analysis (TDA) for bracketing zero-crossings of both one-dimensional continuous functions, and uniformly sampled time series. We present an algorithm and show its robustness in the presence of noise for a range of sampling frequencies. In comparison to state-of-the-art software-based methods for finding zeros of a time series, our method generally converges faster, provides higher accuracy, and is capable of finding all the roots in a given interval instead of converging only to one of them. We also present and compare options for automatically setting the persistence threshold parameter that influences the accurate bracketing of the roots.