Department of Mathematics

Topological Data Analysis

  •  Balija Santoshkumar, MSU
  •  Robust Zero-crossing Detection in Noisy Signals Using Topological Signal Processing
  •  03/22/2021
  •  2:00 PM - 3:00 PM
  •  Online (virtual meeting)
  •  Shelley Kandola (

Detecting zero-crossings in noisy signals is a classical problem that has been researched for over a century. Some of the prominent applications of zero-crossing detection are phase and frequency determination in oscillatory systems, smooth switching operations in power systems, image processing and recognition, speech processing and reconstruction of audio signals, biometrics using human iris, and bar code scanners. This work leverages Topological Signal Processing (TSP), more specifically persistent homology, to develop a simple but powerful zero crossing detection algorithm. The algorithm utilizes zero-dimensional persistent homology to estimate the zero-crossings in a noisy signal, and uses the resulting persistence diagram to find out the significant splits in data to bound the zero crossings. We compare the accuracy and speed of our approach with available methods in the literature using different types of noisy signals, as well as showing sensitivity studies that consider the sampling frequency (SF), and Signal to Noise Ratio (SNR). Our results show that TSP can be directly applied to unfiltered signals with moderate to high noise levels for finding the zero-crossings. In contrast to many existing tools, our approach does not require any complex analog circuitry, iterative solvers, or filtering.



Department of Mathematics
Michigan State University
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