Fundamental component enhancement via adaptive nonlinear activation functions

Stefan Steinerberger, Hau Tieng Wu

Research output: Contribution to journalLetterpeer-review


In many real world oscillatory signals, the fundamental component of a signal f(t) might be weak or does not exist. This makes it difficult to estimate the instantaneous frequency of the signal. A traditional approach is to apply the rectification trick, working with |f(t)| or ReLu(f(t)) instead, to enhance the fundamental component. This raises an interesting question: what type of nonlinear function g:R→R has the property that g(f(t)) has a more pronounced fundamental frequency? g(t)=|t| and g(t)=ReLu(t) seem to work well in practice; we propose a variant of g(t)=1/(1−|t|) and provide a theoretical guarantee. Several simulated signals and real signals are analyzed to demonstrate the performance of the proposed solution.

Original languageEnglish (US)
Pages (from-to)135-143
Number of pages9
JournalApplied and Computational Harmonic Analysis
StatePublished - Mar 2023


  • Activation function
  • Fundamental component
  • Rectification

ASJC Scopus subject areas

  • Applied Mathematics


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