Combination frequencies are not solutions of the perturbed stellar structure equations. In dense power spectra from a light curve of a given multi-periodic pulsating star, they can compromise the mode identification in an asteroseismic analysis, hence they must be treated as spurious frequencies and conveniently removed. In this paper, a method based on fitting the set of frequencies that best describe a general non-linear model, like the Volterra series, is presented. The method allows to extract these frequencies from the power spectrum, so helping to improve the frequency analysis enabling hidden frequencies to emerge from the initially considered as noise. Moreover, the method yields frequencies with uncertainties several orders of magnitude smaller than the Rayleigh dispersion, usually taken as the present error in a standard frequency analysis. Furthermore, it is compatible with the classical counting cycles method, the so-called O-C method, which is valid only for mono-periodic stars. The method opens the possibility to characterise the non-linear behaviour of a given pulsating star by studying in detail the complex generalised transfer functions.

中文翻译：

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从脉动星光曲线中提取非线性的自洽方法——I. 组合频率

组合频率不是扰动恒星结构方程的解。在给定的多周期脉动星的光曲线的密集功率谱中，它们可能会影响星震分析中的模式识别，因此它们必须被视为杂散频率并方便地去除。在本文中，提出了一种基于拟合最能描述一般非线性模型（如 Volterra 级数）的频率集的方法。该方法允许从功率谱中提取这些频率，因此有助于改进频率分析，使隐藏频率能够从最初被认为是噪声中出现。此外，该方法产生的频率具有比瑞利色散小几个数量级的不确定性，通常作为标准频率分析中的当前误差。此外，它与经典的计数周期方法兼容，即所谓的 OC 方法，仅对单周期恒星有效。通过详细研究复杂的广义传递函数，该方法开启了表征给定脉动星的非线性行为的可能性。