利用连续小波变换进行时间序列的信噪比分解：应用于太阳黑子指数
On signal-noise decomposition of timeseries using the continuous wavelet transform: Application to sunspot index
摘要：
我们表明，连续小波变换可以提供一个独特的分解的时间序列中的“信号样”和“噪声样”的组件：从整个小波谱中可以提取两个相互独立的骨架谱，从而允许在甚至非平稳时间序列中单独检测和监测（a）稳定但也瞬态的演变周期性，例如低维动力系统的输出，以及（b）尺度不变结构，例如不连续性、自相似结构或噪声。对月平均太阳黑子指数的一个指示性应用表明，除了众所周知的11年周期外，它的3个谐波，即2年周期，（准两年振荡，QBO）和其他几个（其中一些以前在各种太阳，地球-太阳连接和气候指数中检测到），这里提出的只是QBO的谐波，在所有支持双循环太阳磁发电机模型（Benevolenskaya，1998年，2000年）。尺度最大光谱揭示了太阳黑子数中存在时间尺度长达1年的1/f波动，表明具有这些特征时间尺度的瞬态太阳活动现象中涉及的太阳磁结构处于自组织临界状态（SOC），正如以前提出的太阳耀斑发生（Lu和Hamilton，1991年）。
英文摘要：
We show that the continuous wavelet transform can provide a unique decomposition of a timeseries in to 'signal-like' and 'noise-like' components: From the overall wavelet spectrum two mutually independent skeleton spectra can be extracted, allowing the separate detection and monitoring in even non-stationary timeseries of the evolution of (a) both stable but also transient, evolving periodicities, such as the output of low dimensional dynamical systems and (b) scale-invariant structures, such as discontinuities, self-similar structures or noise. An indicative application to the monthly-averaged sunspot index reveals, apart from the well-known 11-year periodicity, 3 of its harmonics, the 2-year periodicity (quasi-biennial oscillation, QBO) and several more (some of which detected previously in various solar, earth-solar connection and climate indices), here proposed being just harmonics of the QBO, in all supporting the double-cycle solar magnetic dynamo model (Benevolenskaya, 1998, 2000). The scale maximal spectrum reveals the presence of 1/f fluctuations with timescales up to 1 year in the sunspot number, indicating that the solar magnetic configurations involved in the transient solar activity phenomena with those characteristic timescales are in a self-organized-critical state (SOC), as previously proposed for the solar flare occurence (Lu and Hamilton, 1991).
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