Understanding Harmonic Structures Through Instantaneous Frequency.
Understanding Harmonic Structures Through Instantaneous Frequency.
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DOI：
10.1109/ojsp.2022.3198012
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发表时间：
2022
影响因子：
2.8
通讯作者：
中科院分区：
文献类型：
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时间序列数据中的谐波和非正弦波形分析越来越重要。然而，什么构成谐波的精确定义是缺乏的。在本文中，我们提出了一个严格的定义，当考虑信号是在一个谐波关系的基础上的整数频率比，恒定的相位，和一个定义良好的联合瞬时频率。我们发现这个定义是与极值计数和经验模态分解（EMD）。我们探索我们的定义的数学，并将其与解析数论的结果联系起来。这自然导致我们定义两类调和结构，称为强和弱，具有不同的极值行为。我们使用模拟和真实的数据来验证我们的框架。具体来说，我们看看在浅水波的谐波结构，FitzHugh-Nagumo神经元模型，和大鼠海马局部场电位数据的非正弦θ振荡。我们进一步讨论了我们的定义如何有助于解决非线性时间序列分解方法中的模式分裂。清楚地了解谐波何时出现在信号中，将使我们能够更深入地了解非正弦振荡的功能作用。
The analysis of harmonics and non-sinusoidal waveform shape in time-series data is growing in importance. However, a precise definition of what constitutes a harmonic is lacking. In this paper, we propose a rigorous definition of when to consider signals to be in a harmonic relationship based on an integer frequency ratio, constant phase, and a well-defined joint instantaneous frequency. We show this definition is linked to extrema counting and Empirical Mode Decomposition (EMD). We explore the mathematics of our definition and link it to results from analytic number theory. This naturally leads to us to define two classes of harmonic structures, termed strong and weak, with different extrema behaviour. We validate our framework using both simulations and real data. Specifically, we look at the harmonic structures in shallow water waves, the FitzHugh-Nagumo neuronal model, and the non-sinusoidal theta oscillation in rat hippocampus local field potential data. We further discuss how our definition helps to address mode splitting in nonlinear time-series decomposition methods. A clear understanding of when harmonics are present in signals will enable a deeper understanding of the functional roles of non-sinusoidal oscillations.