Fundamental component enhancement via adaptive nonlinear activation functions
Fundamental component enhancement via adaptive nonlinear activation functions
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DOI：
10.1016/j.acha.2022.11.007
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
S. Steinerberger;Hau‐Tieng Wu
中科院分区：
文献类型：
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作者：
S. Steinerberger;Hau‐Tieng Wu
在许多现实世界的振荡信号中，信号 f (t) 的基波分量可能很弱或不存在。这使得估计信号的瞬时频率变得困难。传统的方法是应用纠正技巧，与 | 一起工作。 f(t)|或 ReLu (f (t)) 来代替，以增强基本分量。这就提出了一个有趣的问题：什么类型的非线性函数g:R→R具有g(f(t))具有更明显的基频的性质？ g(t)=| t| g(t)=ReLu(t)在实践中似乎效果很好；我们提出了 g (t)= 1/(1−| t|) 的变体并提供了理论保证。对几个模拟信号和实际信号进行了分析，以证明所提出解决方案的性能。
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.