论文标题
通过随时间变化的波形功能分解非平稳信号
Decomposing non-stationary signals with time-varying wave-shape functions
论文作者
论文摘要
现代时间序列通常由多个振荡组件组成，随着时间变化的频率和振幅受到噪声的污染。如果每个组件具有振荡模式或波形功能，远离正弦函数，并且振荡模式甚至不时变化，则信号处理任务将进一步挑战。实际上，如果存在多个组件，则需要将信号鲁棒分解到每个组件中以出于各种目的，并提取所需的动态信息。在过去的十年中，这种挑战引起了极大的兴趣，但仍然缺乏令人满意的解决方案。我们提出了一种新颖的{\ em非线性回归方案}，以将信号鲁棒分解到其构成多个振荡组件中，并具有时间变化的频率，振幅和波形功能。我们创建了算法{\ em Shape-appaptive模式分解（SAMD）}。除了模拟信号外，我们还将SAMD应用于两个生理信号，阻抗验尸和脑电图。与现有溶液的比较，包括线性回归，基于递归差异的回归和多分辨率模式分解，表明我们的建议可以通过计算效率提供准确而有意义的分解。
Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern, or the wave-shape function, far from a sinusoidal function, and the oscillatory pattern is even changing from time to time. In practice, if multiple components exist, it is desirable to robustly decompose the signal into each component for various purposes, and extract desired dynamics information. Such challenges have raised a significant amount of interest in the past decade, but a satisfactory solution is still lacking. We propose a novel {\em nonlinear regression scheme} to robustly decompose a signal into its constituting multiple oscillatory components with time-varying frequency, amplitude and wave-shape function. We coined the algorithm {\em shape-adaptive mode decomposition (SAMD)}. In addition to simulated signals, we apply SAMD to two physiological signals, impedance pneumography and electroencephalography. Comparison with existing solutions, including linear regression, recursive diffeomorphism-based regression and multiresolution mode decomposition, shows that our proposal can provide an accurate and meaningful decomposition with computational efficiency.
