高階頻譜分析應用於腦電波特徵描述

Abstract

在過去二十年來,傳統的複利葉轉換廣泛的應用於各種訊號的頻譜分析，但是對於含有複雜頻譜的訊號，則無法有效的特徵萃取，例如腦電波。在這篇論文中，我們將高階頻譜當作腦電波特徵抽取的工具。我們希望藉著設計特別的量化方法，來探索腦電波隱藏在高階頻譜上的特徵。 首先，我們使用高階頻譜來抽取單一通道的腦電波。這分析包括: (1)研究高階頻譜中相位的資訊，(2)識別四種基本型態的腦電波在高階頻譜上的特徵，(3)利用高階頻譜來萃取和量化beta波的特徵。(一個研究的例子) 接下來，我們使用的高階頻譜(cross-bispectrum)來抽取多通的腦電波，這分析包括: (1)研究高階頻譜中相位的資訊，(2)識別取自不同通道四種基本型態的腦電波在高階頻譜(cross-bispectrum)上的特徵，(3)研究alpha波在時間和空間的動態特徵。 相對於傳統的複利葉分析方法，這篇論文的研究結果顯示高階頻譜的優點: 含有相位的資訊,對於混合波型且複雜的腦電波，高階頻譜能提供良好的特徵。針對不同的應用,可以藉著不同的量化方法得到較好的特徵。

In the past 20 years, the traditional Fourier transformation has been widely applied to spectral analysis of a variety of signals. However, Fourier transformation is not sufficient for analyzing the signals of complicated spectrum, like the EEG (electroencephalography). In this thesis, we use the bispectrum as a tool to characterize the EEG features. We investigate the features of EEG revealed in it’s bispectrum and cross-bispectrum using particularly designed quantification method. First, we analyze the bispectrum of one-channel EEG. The research includes (1) studying the phase information explored by the bispectrum,(2) identifying the bispectral features of the four fundamental rhythms of EEG, and (3) extracting and quantifying the features of beta rhythm by the bispectrum (a case study). Next, we analyze the cross-bispectrum of multi-channel EEG. The research includes (1) studying the phase information explored by the cross-bispectrum, (2) identifying the cross-bispectral features of the four fundamental rhythms of EEG appearing in different channels,.and (3) exploring the dynamic feature of alpha rhythms temporally and spatially. The results of this thesis demonstrate the advantage of bispectral analysis in comparison with the conventional FT analysis. Bispectral analysis contains phase information and may provide a robust approach for analyzing the weak-rhythmic, complicated EEG signals. Difference quantative approaches may be designed for various applications.