Fundamental component enhancement via adaptive nonlinear activation functions

TL;DR

This paper investigates adaptive nonlinear activation functions to enhance the fundamental component of oscillatory signals, proposing a novel function with theoretical guarantees and demonstrating improved frequency estimation on simulated and real signals.

Contribution

It introduces a new adaptive nonlinear function for fundamental component enhancement with theoretical analysis and practical validation.

Findings

The proposed function improves fundamental frequency prominence.

The method outperforms traditional rectification techniques.

Validated on both simulated and real-world signals.

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.