經驗模態分解是一種自適性的訊號拆解方法。其拆解訊號的基底函數取決於訊號本身，因此常被應用於非線性與非穩態的生理訊號上。訊號可因此被解構成數個具有物理意義的本質模態函數(IMF)並加以分析。 經驗模態分解演算法在輸出固定數量之本質模態函數時，其計算複雜度雖為O(n)，但記憶體複雜度與傳統時頻分析如傅立葉轉換、小波轉換等相比還是相對大。因此如將其應用在記憶體有限的穿戴式嵌入式裝置中即時運算時，訊號的輸入長度會被限制，導致其無法萃取出有物理意義的低頻本質模態函數。 因此本研究將以另類的滑移視窗演算法，在不增加其計算複雜度下對經驗模態分解演算法的記憶體複雜度最佳化。並且證明該滑移視窗演算法的計算結果與原始經驗模態分解演算法一致，使記憶體複雜度得以由(13+n_IMF)n降至(2+n_out)n。 除此之外，由於嵌入式系統取樣時所產生的雜訊會使經驗模態分解的結果產生模態混合。為了解決此問題，需使用擾動輔助的經驗模態分解演算法如總體經驗模態分解法、互補總體經驗模態分解法與均相經驗模態分解等。因此本研究將應用低記憶體的經驗模態分解到上述之擾動輔助經驗模態分解中，並於穿戴式嵌入式裝置即時運算以驗證其計算結果與時間。 ;Empirical mode decomposition (EMD) is an adaptive signal decomposition method. The basis function of the empirical mode decomposition depends on the input signal, so it is often applied to nonlinear and nonstationary biomedical signals. When the empirical mode decomposition algorithm outputs a fixed number of intrinsic mode functions (IMF), its computational complexity is O(n). However, the memory complexity is larger than traditional time-frequency analysis such as Fourier transform and wavelet transform. Therefore, When EMD is applied to real-time computing in a memory-limited wearable embedded device, the length of input signal will be limited. As a result, EMD cannot extract the low-frequency intrinsic mode function. Therefore, this research will propose an alternative sliding window algorithm to optimize the memory complexity of EMD algorithm without increasing its computational complexity. The memory complexity can be reduced from (13+n_IMF)n to (2+n_out)n. And it will prove that the calculation result of the sliding window algorithm is consistent with the original empirical mode decomposition algorithm. In addition, due to the sampling noise of embedded system, the EMD will cause mode-mixing in IMF. In order to solve this problem, the disturbance-assisted empirical mode decomposition algorithms such as ensemble empirical mode decomposition, complementary ensemble empirical mode decomposition and uniform phase empirical mode decomposition are used. In this study, the low memory empirical mode decomposition is applied to disturbance-assisted empirical mode decomposition, and then we will verify the results and run-time in the wearable embedded devices.
