高清晰時頻分析法及衛星訊號分析與帕金森凝步偵測

Abstract

傳統上分析訊號頻率常使用傅立葉轉換，然而其只適用於穩態的線 性訊號上，故近代發展出針對非穩態訊號的時頻分析工具。時頻分析 可觀察信號隨時間的頻率變化，運用範圍日趨廣泛，但時頻圖的解析 度、交叉項與運算量的取捨一直是時頻研究的重點。 本論文針對此問題提出了一個高清晰度的修正廣義頻譜圖，藉由採 用不同大小的窗格與次方項讓時域與頻域的解析度能同時提高。另外 針對寬窗格的情況，我們則提出新的轉換方式以減少運算量。而窗格 的取法，我們亦提出較佳的取法來做更一般化的選取。再者，我們將 此新方法與多項式韋格納—韋立分佈做結合，提出一個新的廣義多項 式韋格納頻譜圖，用以改良傳統的賈伯—韋格納轉換，並且得到更好 的解析度成果。 時頻理論的應用則分為兩大部分： 第一部分為福爾摩沙衛星三號的訊號分析，此部分是與國家太空中 心合作的計畫。我們利用希爾伯特—黃轉換與時頻分析方法，找出衛 星元件老化的趨勢與關鍵因素，並希望使用的可適性方法在未來的衛 星上能有效發揮，提早看出老化趨勢。 第二部分則為帕金森氏症凝凍步態偵測的演算法，此部分為與臺大 物理治療所與慈濟大學合作的計畫，目的是希望藉由時頻分析改良現 有的凝步偵測方法，以提升判斷準確度與更即時的症狀偵測。我們利 用廣義頻譜圖求出凝凍指標，並考慮輸入訊號的能量變化來做進一步 的判斷，再藉由動態閥值找出凝凍步態的發生區段。另外我們使用非 對稱窗格來減少未來資訊的使用，讓判斷時間延遲僅有0.8 秒。我們的 方法達到即時偵測與效果勝出既有方法，並期望在未來實作於產品上 造福更多帕金森氏症患者。

Traditionally, we usually use the Fourier transform to analyze the frequency of a signal. However, it is only suitable for the case where signals are stationary and linear. Thus, many time-frequency (TF) analysis tools were developed for non-stationary signals in recently decades. TF analysis can observe the signal variation in both the time and the frequency domains and has many applications. However, there are always trade-offs among the goals of high resolution, no cross term, and less computation time. In this thesis, we propose a high-clarity modified generalized spectrogram (MGS) with different window sizes and different powers, which can get both high resolutions in the time and the frequency domains. We also provide a new implementation way to reduce the computation time for the broad window case and propose a better method to choose the window. Moreover, we propose a new method called the generalized polynomial Wigner spectrogram (GPWS), which combines the MGS with the polynomial Wigner-Ville distribution (PWVD), to further improve the performance of the Gabor-Wigner transform (GWT). Two applications of the TF theory are introduced in this thesis: The first application is the analysis of the FORMOSAT-3/COSMIC (F3/ C) signal. It is a cooperation project with the National Space Organization (NSPO). Instead of the traditional trending method, the Hilbert-Huang transform (HHT) and time-frequency analysis are used to analyze the trends of the signals from the F3/C constellation and the deterioration on some key satellite elements. The goal of these adaptive analysis methods is to effectively find the aging trends of satellites. The second application is to detect the freezing of gait (FOG) of Parkinson's disease patients. It is a cooperation project with the Graduate Institute of Physical Therapy of National Taiwan University (NTU-PT) and the Tzu-Chi University. The purpose is to improve the detection accuracy of the FOG and develop a more real-time algorithm by using TF analysis. We use the MGS to find the freezing index (FI) and consider the power of the input 3-D accelerator signal for the further decision. With a dynamic threshold, FOG periods can be found. Since existing methods use the symmetric window, which will cause a severe delay, we use an asymmetric window and an asymmetric smooth filter to make the delay less than 0.8 seconds. Our method is real-time and the performance still outperforms existing methods. The ultimate goal is to implement the algorithm in products and benefit Parkinson's disease patients.