WD應用於濾波器特性分析與腦波暫態特性分析

Abstract

在分析特性隨時間而變(nonstationary)之訊號的領域上，時間頻率表示 法(time-frequency representation,TFR)是一個被廣泛使用的方法。有 許多表示法能將能量密度同時表示於時間與頻率的平面上,而Wigner distribution(WD)是其中之一。首先，我們使用WD方法和傳統方法來分析 濾波器特性。根據實例與分析的結果，我們發現時間頻率表示法能較完整 地描述訊號和系統的特徵。特別是當訊號或或系統具有暫態、頻率相關之 特徵時，WD提供了一個萃取這類特徵之合適工具。接著，我們使用WVD和 瞬間頻率(IF)的觀念來偵測腦波(EEG)中集中型放電波的發生 。並且比較 WVD方法和短時間傅立葉轉換法 (STFT method)的偵測結果。結果顯示WVD 方法略優於STFT method。在此， 比較的準則是依據暫態特殊波形被偵測 出來的正確率。此外，我們使用WVD方法和計算IF來探討多頻道EEG的頻道 相關性與空間特徵。我們發現在偵測多頻道EEG的暫態特殊波形上有兩個 重要的因素：其一是計算WVD和STFT時使用的視窗長度(window length)； 另一個是訊號的錄製位置。根據我們的實驗可知，較適於用來分析的訊號 錄製點是靠近其產生暫態波形的發生源(source)。 Time-frequency representation is a widely used method in the field of analyzing nonstationary signal. Wigner distribution (WD) is one of many representations capable of displaying energy density information on time-frequency plane. First of all, WD method and conventional method are applied to the analysis of filters' characteristics. According to those examples and results presented, we find that characteristics of signals and systems are better revealed with time-frequency distribution. Especially when transient, frequency-dependent characteristics are of interest, WD provides a useful tool to extract those features. Then, WVD and the concept of instantaneous frequency (IF) are used to detect transient events of focal sharp waves in EEG. We will compare the results obtained with WVD method and STFT method. The performance using WVD is better than using STFT method. The performance is evaluated by the capability of correctly detecting the events of interest. In addition, channel correlation and spatial characteristics of multichannel EEG's are studied using WVD method with the aid of IF estimation. We find that there are two important factors in detecting the transient events of multichannel EEG's. One factor is the window length used for computing WVD and STFT. The other factor is the recording site of the signal. Based on our experiments, an appropriate choice of the EEG channel is the one close to the source generating the events.