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Abstract: self-similarity or scale-invariance is a fascinating characteristic found in various signals including electroencephalogram (EEG) signals. A common measure used for characterizing self-similarity or scale-invariance is the spectral exponent. In this study, a computational method for estimating the spectral exponent based on wavelet transform was examined. A series of Daubechies wavelet bases with various numbers of vanishing moments were applied to analyze the self-similar characteristics of intracranial EEG data corresponding to different pathological states of the brain, i.e., ictal and interictal states, in patients with epilepsy. The computational results show that the spectral exponents of intracranial EEG signals obtained during epileptic seizure activity tend to be higher than those obtained during non-seizure periods. This suggests that the intracranial EEG signals obtained during epileptic seizure activity tend to be more self-similar than those obtained during non-seizure periods. The computational results obtained using the wavelet-based approach were validated by comparison with results obtained using the power spectrum method.

基于小波分析的癫痫脑电图自相似性测量

自相似性或尺度不变性是信号（包括脑电图信号）中的一个重要特征。本文基于小波变换介绍一种估计谱指数的计算方法。 提出1/过程基于小波分析的表征，验证其能有效估计用于表征自相似性的谱指数。 引入频域分析中的1/过程，介绍其基于小波分析的表征，提出基于小波分析的自相似性测量基本步骤。通过数据分析验证所提方法的正确性（图3-6）。 计算结果表明基于小波分析的1/过程能够有效估计表征自相似性的谱指数。小波变换方法适用于自相似或尺度不变的信号。基于小波分析估计得到的颅内脑电图信号谱指数与功率谱方法估计得到的数据相差无几。癫痫惊厥时较之非惊厥时段获取的颅内脑电图信号具有更高的自相似性。
自相似性；幂律行为；小波分析；脑电图；癫痫；惊厥

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