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 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 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.

中文翻译：

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用时变波形函数分解非平稳信号

现代时间序列通常由多个振荡分量组成，时变频率和幅度被噪声污染。如果每个组件都具有振荡模式或波形函数，远离正弦函数，并且振荡模式甚至不时发生变化，则信号处理任务将面临进一步挑战。在实践中，如果存在多个分量，则需要出于各种目的将信号稳健地分解为每个分量，并提取所需的动态信息。在过去十年中，此类挑战引起了极大的兴趣，但仍然缺乏令人满意的解决方案。我们推荐一本小说非线性回归方案，将信号稳健地分解为具有时变频率、幅度和波形函数的多个振荡分量。我们创造了算法形状自适应模式分解（SAMD）。除了模拟信号外，我们还将 SAMD 应用于两个生理信号，阻抗肺描记和脑电图。与现有解决方案（包括线性回归、基于递归微分同胚的回归和多分辨率模式分解）的比较表明，我们的提议可以提供准确且有意义的分解和计算效率。