Fundamental component enhancement via adaptive nonlinear activation functions

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.