Singular spectrum analysis (SSA) has been verified to be an effective method for decomposing non-stationary signals. The decomposition and reconstruction stages can be interpreted as a zero-phase filtering process where reconstructed components are obtained by inputting a signal through moving average filters. However, mathematical analysis indicates that the use of a default rectangular window in the embedding stage would corrupt the frequency characteristics of the trajectory matrix, resulting in spectral leakage. To attenuate the effect of spectral leakage and to obtain more concentrated SSA components, this study introduces a windowing technique in SSA, called generalized singular spectrum analysis (GSSA). In GSSA, the default rectangular window is replaced with adjustable taper windows, which are widely used for attenuating spectral leakage. Through windowing, GSSA can achieve less spectral leakage, and produce more energy-concentrated reconstructed components compared with conventional SSA. Grouped spectral entropy (GSE) is used as the metric for evaluating the performance of the proposed GSSA algorithm. Results from experiments, which were conducted on a synthetic signal and two real electroencephalogram signals, show that GSSA outperforms the conventional SSA and the baseline in the reduction of spectral leakage. Compared with the baseline, the proposed GSSA achieves a lower averaged GSE, resulting in reduction of 0.4 for eigenfilters and 0.11 for reconstructed components, respectively. Our results reveal the effectiveness of GSSA in the decomposition and analysis of non-stationary signals.

中文翻译：

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用于非平稳信号分解和分析的广义奇异谱分析

奇异谱分析（SSA）已被证明是分解非平稳信号的有效方法。分解和重构阶段可以解释为零相位滤波过程，其中通过移动平均滤波器输入信号来获得重构分量。然而，数学分析表明，在嵌入阶段使用默认矩形窗口会破坏轨迹矩阵的频率特性，导致频谱泄漏。为了减弱频谱泄漏的影响并获得更集中的 SSA 分量，本研究在 SSA 中引入了一种加窗技术，称为广义奇异频谱分析 (GSSA)。在 GSSA 中，默认的矩形窗口被可调节的锥形窗口取代，广泛用于衰减频谱泄漏。与传统的SSA相比，通过加窗，GSSA可以实现更少的光谱泄漏，并产生更多能量集中的重构分量。分组谱熵（GSE）用作评估所提出的 GSSA 算法性能的指标。对合成信号和两个真实脑电图信号进行的实验结果表明，GSSA 在减少频谱泄漏方面优于传统 SSA 和基线。与基线相比，所提出的 GSSA 实现了较低的平均 GSE，导致特征滤波器和重构组件分别减少 0.4 和 0.11。我们的结果揭示了 GSSA 在非平稳信号分解和分析中的有效性。