綜合多變量的多尺度熵分析法

Abstract

熵是度量訊號複雜程度的方法，為了瞭解訊號中複雜度的結構性，在多個尺度上分析複雜度變化是目前熵分析的趨勢。Costa, M.提出時間尺度上的多尺度分析法，在多個領域上取得值得肯定的成果，但這些尺度多為訊號的低頻分量，無法解讀出訊號高頻層次的訊息。頻率域的多尺度熵分析法也隨之發展，利用黃鍔博士提出的經驗模態分解，產生不同頻帶的本質模態函數，將本質模態函數作層次的疊加，產生頻率域的尺度，但這些尺度缺乏客觀的度量，無法明確定位。 本於本質模態函數所包含的瞬時狀態，利用其瞬時頻率與瞬時振幅建構出基於瞬時頻率功率譜估計，本文提出在此功率譜上，藉由尺度訊號的分佈特性，擷取各頻率尺度的位置與寬度特徵，並以3個參數來描述尺度訊號：頻譜位置、分佈寬度與尺度複雜度，更完整地定義尺度訊號。在研究中，除了使用FM訊號、噪訊、含噪訊的正弦波訊號來觀察其多尺度熵趨勢，還使用受35Hz視覺刺激與休息時的兩種狀態的穩態視覺誘發電位訊號作為對照，在3維的尺度參數軸上，比較其多尺度熵趨勢變化。並在接近閃爍頻率的頻帶中，觀察到多尺度熵趨勢在受視覺刺激時，因腦內產生相對應的頻率反應，使腦狀態的複雜度較休息時降低，對不同的腦狀態作出解讀。除此之外，使用分佈參數來描述尺度訊號，較目前使用尺度指標更能反映尺度訊號的特徵，並為不同種類訊號的多尺度熵比較提供了客觀度量的基礎，使頻率域的多尺度熵分析趨於完整。

Entropy is used for measuring signal complexity. In order to understand the structural complexity of a signal, analysis of the complexity changes in multiple scales is the trend of entropy study. Costa, M. proposed the multiscale entropy analysis in time domain, but these low-frequency scales are unable to reveal the high-frequency information of the signal. The multiscale entropy analysis in frequency domain is soon developed. Use Empirical Mode Decomposition proposed by Norden E. Huang, extracting Intrinsic Mode Functions from the signal in different frequency band. Therefore, frequency scales are obtained by the cumulative sums of the intrinsic mode functions. But without objective measurements, these scales cannot be considered as explicitly defined. Because of the transient nature of intrinsic mode function, the Instantaneous Frequency inferred Power Spectral Density is used. We capture the features of scales by extracting the position and spread parameter of the distribution of scale signals in the PSD. The signal of each scale is described with three parameters: the position and the spread of the distribution, the complexity of the signal. In this research, we use frequency modulate signal, noise and noisy sinusoidal signal as examples to distinguish the trend of each signal. Also we use two status of Steady State Visually Evoked Potential signal: under 35Hz flickering stimuli and rest, then observe the trend of each status. We do notice the entropy decrease in the trend of stimuli frequency band, due to the potential response under stimulated state. Most important of all, this research provides an objective basis for multiscale entropy comparison between signals by capturing scale features of distribution in IF inferred PSD instead of using index. As a result, the multiscale entropy analysis of frequency domain tends to be completed.