小波分析應用於多頻道腦波訊號

Abstract

在分析特性隨時間而變(nonstationary)之訊號時，時間一頻率表示法(time frequency representation)是一個廣泛被使用的方法。在本篇論文中，我們使用一種時間一頻率表示法：小波轉換(wavelet transform)，來分析具有集中性放電波的多頻道腦波訊號(Multi-channel EEG)。 由傳統的傳立葉轉換，我們無法觀察到腦波訊號中頻譜隨時間變化的特性。而短時間傳立葉轉換(short-time Fourier transform)，它雖然同時提供我們時間和頻率的資訊，但只具有固定的解析度。小波轉換利用可變的時間及頻率解析度，來分析訊號中的各種成份。在此，我們首先探討以數學模型為主波的腦波訊號的小波轉換特性，由不同主波所產生的不同小波轉換中，我們不禁要問：對於一組特殊訊號，到底那一個主波才是適當的？為了瞭解這個問題，我們利用次頻編碼(subband coding scheme)的方法，分離腦波訊號中具有特殊意義的暫態波形。來研究分離出來的腦波成份作主波(EEG wavelet)所產生小波轉換的特性。因為小波分析是測量訊號和主波的相似性(similarity)，此研究可以得到同一頻道及不同頻道的腦波訊號特性作為將來病源處活動變化的探討。

Time-frequency representation (TFR) is a widely used method in the field of analyzing nonstationary signals. In this thesis, we analyze multi-channel EEG (electroencephalograph) signals having focal sharp wave activities using wavelet transformation (WT), one of the TFR method. from the traditional Fourier transform (FT), we can not observe any information respecting to the time-varying frequency contents in EEG. On the other hand, short-time Fourier transform (STFT) provides time and frequency information simultaneously, but with fixed frequency resolution. Wavelet transform is one of TFR with varied time/frequency resolution Adapted fro delicate and coarse components of signals. In this study, we begin with exploration of EEG’s CWT (continuous WT) properties using mother wavelet prototype generated from well-known mathematical models. Observing differences in CWTs resulted from different mother wavelets, we might question what is an appropriate mother wavelet prototype for a particular signal? To approach this problem, subband coding scheme is utilized to extract and purify a component directly from the transient event of interest in EEG signal. Hence, the study focus on CWT characteristics with mother wavelet prototype derived from the extracted component (called “EEG wavelet”). Since CWT in a sense measures the similarity between mother wavelet and the EEG epoch to be analyzed, this study is also devoted to characterization of inter-and intra-electrode features in multi-channel EEG, from which the focal source activity might be explored in the future.