Source signals often contain various hidden waveforms, which further provide precious information. Therefore, detecting and capturing these waveforms is very important. For signal decomposition (SD), discrete Fourier transform (DFT) and empirical mode decomposition (EMD) are two main tools. They both can easily decompose any source signal into different components. DFT is based on Cosine functions; EMD is based on a collection of intrinsic mode functions (IMFs). With the help of Cosine functions and IMFs respectively, DFT and EMD can extract additional information from sensed signals. However, due to a considerably finite frequency resolution, EMD easily causes frequency mixing. Although DFT has a larger frequency resolution than EMD, its resolution is also finite. To effectively detect and capture hidden waveforms, we use an optimization algorithm, differential evolution (DE), to decompose. The technique is called SD by DE (SDDE). In contrast, SDDE has an infinite frequency resolution, and hence it has the opportunity to exactly decompose. Our proposed SDDE approach is the first tool of directly applying an optimization algorithm to signal decomposition in which the main components of source signals can be determined. For source signals from four combinations of three periodic waves, our experimental results in the absence of noise show that the proposed SDDE approach can exactly or almost exactly determine their corresponding separate components. Even in the presence of white noise, our proposed SDDE approach is still able to determine the main components. However, DFT usually generates spurious main components; EMD cannot decompose well and is easily affected by white noise. According to the superior experimental performance, our proposed SDDE approach can be widely used in the future to explore various signals for more valuable information.

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一种优化算法来检测信号的隐藏波形

源信号通常包含各种隐藏的波形，这些波形进一步提供了宝贵的信息。因此，检测和捕获这些波形非常重要。对于信号分解（SD），离散傅里叶变换（DFT）和经验模式分解（EMD）是两个主要工具。它们都可以轻松地将任何源信号分解为不同的分量。DFT基于余弦函数；EMD基于固有模式函数（IMF）的集合。分别借助余弦函数和IMF，DFT和EMD可以从感测到的信号中提取其他信息。然而，由于相当有限的频率分辨率，EMD容易引起频率混合。尽管DFT具有比EMD更大的频率分辨率，但其分辨率也是有限的。为了有效地检测和捕获隐藏的波形，我们使用优化算法差分演化（DE）进行分解。该技术称为DE的SD（SDDE）。相反，SDDE具有无限的频率分辨率，因此有机会进行精确分解。我们提出的SDDE方法是将优化算法直接应用于信号分解的第一个工具，在信号分解中可以确定源信号的主要成分。对于来自三个周期波的四个组合的源信号，我们在没有噪声的情况下的实验结果表明，所提出的SDDE方法可以准确或几乎准确地确定其相应的独立分量。即使存在白噪声，我们提出的SDDE方法仍然能够确定主要成分。但是，DFT通常会生成虚假的主要成分。EMD不能很好地分解，很容易受到白噪声的影响。根据卓越的实验性能，我们提出的SDDE方法可以在将来广泛用于探索各种信号以获得更有价值的信息。