Math @ Duke
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Publications [#361465] of Hau-Tieng Wu
Papers Published
- Steinerberger, S; Wu, H-T, Fundamental component enhancement via adaptive nonlinear activation
functions
(December, 2021)
(last updated on 2024/04/19)
Abstract: 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 $\mbox{ReLu}(f(t))$ instead, to
enhance the fundamental component. This raises an interesting question: what
type of nonlinear function $g:\mathbb{R} \rightarrow \mathbb{R}$ has the
property that $g(f(t))$ has a more pronounced fundamental frequency? $g(t) =
|t|$ and $g(t) = \mbox{ReLu}(t)$ 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.
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