小波係數應用於腦電波之特徵分析

Abstract

在一般自然界中的訊號，其頻率成份都會隨時間而改變，是故時間－ 頻率表示法( Time-Frequency representation)已廣為使用。本論文中， 我們亦將採用一種時間－頻率表示法，即小波轉換( Wavelet Transform) ，來分析腦波訊號(EEG)。 一段訊號經過各種不同尺度 (scale)的小波轉換後，將會產生一個大量的 二維資料。而在此二維的龐大資訊量下，期望可以經由進一步量化而找出 幾個具代表性的結果，幫助我們瞭解原來的腦波訊號。所以本論文的目的 ，除了對原訊號做小波轉換外，即在於提出一些特徵量化的方法，來幫助 我們由各個角度來探究腦波訊號。於本文中分別運用了碎形維度( Fractal Dimension)、相互資訊( Mutual Information)、交互相關( Cross-Correlation)等方法來對不同尺度(scale)下的小波轉換結果( 或 稱小波係數、Wavelet Coefficients)進行分析。 經過驗證，碎形維度、交互相關等法則皆可得到定性與定量上的成效。而 相互資訊因為漏失了時序資料，故無法歸納一個滿意的結果。 Most signals in nature have the spectral property which is time-varying. So the Time-Frequency representation is widely used. In this thesis, we will introduce a time-frequency representation method,Wavelet Transform(WT),to analyze the EEG signals. A signal processed by the wavelet transform will result in a two-dimensional atadata array with lots of parameters. From this large amount of parameters,we would like to obtain a few substantial coefficients using some quantitative approaches. So the purpose of this thesis is to introduce some quantitative methods and to explore the characteristics of EEG signal from various viewpoints,in addition to transforming the original signal by wavelet transform . In the thesis,we apply the Fractal Dimension、Mutual Information and Corss- correlation methods to analysis of wavelet coefficients of different scales. From our experiment, methods of the Fractal Dimension、Cross- correlation provide a way to qualitatively and quantitatively characterize and the EEG*s. Nevertheless, the Mutual Information method suppressing the temporal information is not a feasible tool for quantifying the WT coefficients.