Fundamental component enhancement via adaptive nonlinear activation functions

by   Stefan Steinerberger, et al.
Duke University
University of Washington

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. Traditionally, researchers apply the rectification trick, working with |f(t)| or (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) = (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.


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