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    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/70367

    Title: 利用數值模擬探討各式干擾因子對兩電生理訊號因果關係判讀之影響
    Authors: 李秉儒,;Li,Ping-ju
    Contributors: 數學系
    Keywords: 時間偏移;相位偏移;振幅脹縮;雜訊水平;因果性
    Date: 2016-05-04
    Issue Date: 2016-06-04 15:55:47 (UTC+8)
    Publisher: 國立中央大學
    Abstract: 本研究以兩種可以從生物體測得的電生理訊號為模擬對象,如腦電波、場電位、血壓等,探討其因果性參數受訊號誤差之干擾而失真的程度。因此,利用數值模型來模擬以下四種干擾因子:時間偏移 ( Time Shift )、相位偏移 ( Phase Shift )、振幅脹縮 ( Amplitude Expansion Or Contraction ) 與雜訊水平 ( Noise Level )。模擬的方式為,計算低頻訊號 x 和受干擾之高頻訊號 y 之間的因果係數,對原本的係數造成多大的影響。

    分析結果顯示,由單一因子模擬,發現作用在高頻訊號的四種干擾因子,對因果關係的影響程度由小到大依序為振幅脹縮、時間偏移、相位偏移及雜訊水平。也就是說,振幅脹縮此因子的表現,相較於其他三者,對因果係數的影響最小,雜訊水平的影響最大。從雙因子模擬,當固定時間偏移這個因子時,可以觀察到因果關係對於雜訊水平的容忍度縮小許多,只要雜訊水平強度稍大,就足以影響訊號波形,進而影響到因果關係的判別。最後,我們依照模擬的結果,列出四種干擾因子隨其干擾程度範圍擴大的影響趨勢,提供讀者參考使用。本研究以生物體內兩種在生物體內可以得到的兩種電位生理訊號為模擬對象,如腦電波、場電位、血壓等,在探討其因果性時,可能因實驗誤差而造成失真,進而影響判讀結果的程度。因此,利用數值模擬,探討以下四種干擾因子:時間偏移延遲 ( Time Lag )、相位偏移 ( Phase Shift )、振幅脹縮 ( Amplitude Expansion Or Contraction )、雜訊水平 ( Noise Level ) ,若發生在低頻訊號 x 和高頻訊號 y 兩者間,對於原本GCI該有的數值會造成多大的影響。

    分析結果顯示,由單一因子模擬,可以發現四種擾因子對低頻訊號 x 和高頻訊號 y 兩者間的因果關係,其影響程度大小依序為振幅脹縮、時間偏移延遲、相位偏移及雜訊水平。也就是說,振幅脹縮此因子的表現,相較於其他三者,對GCI的影響最小,雜訊水平對GCI的影響最大。從雙因子模擬,當固定時間延遲偏移這個干擾因子時,可以觀察到因果關係雜訊水平對於雜訊水平因果關係的容忍度較小許多,只要雜訊水平強度稍大,就足以影響訊號波形,進而影響到GCI的判別。
    ;In this study, we take two electrophysiological signals obtained from organisms as examples, such as EEG, local field potential, blood pressure, etc. When we investigate Granger causality, it may be distorted by experimental error from input data. Then it will affect the result of Granger causality. Accordingly, we use numerical simulation to inquire four interfering factors: Time shift, phase shift, amplitude expansion or contraction and noise level. By this way, we will know how much impact will be on the values of the original Granger causality index when those factors occur on the high-frequency signal.

    The results show that, we can find four interfering factors on the causality between the low-frequency signal x and the high-frequency signal y from the single factor simulations. The influence level from the least to the worst is amplitude expansion or contraction, time shift, phase shift, and noise level. In other words, we find the performance of amplitude expansion or contraction is more robust than other three interfering factors, because its impact on GCI is minimal. On the other hand, noise level has maximal impact on GCI. Then, by two-factor simulations, when we fix the factor of time shift, we can observe the GCI decline curve decreasing faster than other three factors. It also shows that the noise level has the smallest tolerance of input errors. If the strength of noise level is larger, it is enough to affect the signal waveform and impact to interpret the result of Granger causality.

    Finally, we construct a mathematical model and the estimation formula of standard deviation of four interfering factors. According to the results of the simulation, we give the range of standard deviations of four interfering factors for the readers’ reference.
    Appears in Collections:[數學研究所] 博碩士論文

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