🍩 Database of Original & Non-Theoretical Uses of Topology

1. Robust Crossings Detection in Noisy Signals Using Topological Signal Processing (2024)

   Sunia Tanweer, Firas A. Khasawneh, Elizabeth Munch

   Abstract

   This article explores a novel method of bracketing zero-crossings for both 1-D functions and discretely sampled time series by the application of 0-D persistent homology from algebraic topology. We introduce an algorithm and demonstrate its capability of detecting crossing in noisy signals across various sampling frequencies. Compared to other software-based methods for crossing-detection in signals, our approach is typically faster, shows a higher accuracy, and has the unique ability to identify all roots within the provided interval instead of detecting only one out of all. We also discuss different options for mathematically estimating the persistence threshold— a parameter which impacts and controls the correct bracketing of roots. Finally, we explore the potential of extending our algorithm to higher dimensions.

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   • Signal Processing
   • array
   • signal
   • Confirm
   • persistent homology
   • persistent homology:persistence diagrams