經驗模態分解能根據訊號本身的特性提取具有物理意義的本質模態函數。因此在處理複雜的語音訊號時，經驗模態分解具有顯著的優勢。然而經驗模態分解提取的本質模態函數經常出現模態混合現象，導致其物理意義受損。因此許多擾動輔助經驗模態分解被提出，例如總體經驗模態分解與均勻相位經驗模態分解，來改善此問題。儘管擾動輔助經驗模態分解在處理非線性及非平穩訊號方面具有優勢，但其高運算量與記憶體需求對資源有限的嵌入式系統構成挑戰。在本研究將評估擾動輔助經驗模態分解演算法在嵌入式穿戴裝置中常用的微控制器中即時處理語音訊號的可行性，並在符合即時語音處理限制的條件下進行最佳化以降低計算時間、記憶體需求與系統延遲。經過最佳化，研究結果顯示，使用即時自適應擾動輔助經驗模態分解演算法進行語音除噪時，對於採樣頻率為16k Hz的語音訊號，計算負載比達54%、音訊延遲為0.03秒，記憶體需求為18.75 KB；而進行語音特徵處理時，對於8k Hz的語音訊號，計算負載比為59.67%、音訊延遲為0.1697秒，記憶體需求為68.75 KB。雖然在微控制器上實現以擾動輔助經驗模態分解進行即時語音處理具有可行性，但計算量與音訊延遲依舊是很大的問題。

Empirical Mode Decomposition (EMD) extracts intrinsic mode functions (IMFs) with physical significance based on the signal's characteristics, making it advantageous for complex speech signal processing. However, EMD often suffers from mode mixing, which undermines its physical interpretation. To address this, disturbance-assisted EMD (DA-EMD) methods like Ensemble EMD (EEMD) and Uniform Phase EMD (UPEMD) have been proposed. While DA-EMD excels in handling nonlinear, non-stationary signals, its high computational load and memory requirements pose challenges for resource-limited embedded systems. This study evaluates the feasibility of implementing DA-EMD for real-time speech processing on microcontrollers (MCUs) in embedded wearable devices, optimizing it to reduce computation time, memory usage, and system latency. The optimized Real-Time UPEMDA algorithm demonstrated a 54% computational load, 0.03-second audio delay, and 18.75 KB memory usage for 16kHz speech denoising. For 8kHz speech feature extraction, the computational load was 59.67%, with a 0.1697-second delay and 68.75 KB memory usage.

［1］ Lee, W. T., “Tridiagonal matrices: Thomas algorithm,” MS6021, Scientific Computation, University of Limerick, 2011.
［2］ Huang, Norden E., et al. “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 454, no. 1971, pp. 903-995, 1998.
［3］ Wang, Yung-Hung, et al., “On the computational complexity of the empirical mode decomposition algorithm. ” Physica A: Statistical Mechanics and its Applications, vol. 400, pp. 159-167, 2014.
［4］ Wang, Y. H., Lin, Y. C., “On the memory cost of EMD algorithm.” IEEE Access, vol. 10, pp. 114242-114251, 2022.
［5］ Huang, Norden E., Zheng Shen, and Steven R. Long, “A new view of nonlinear water waves: the Hilbert spectrum,” Annual Review of Fluid Mechanics, vol. 31, no. 1, pp. 417-457, 1999.
［6］ Wu, Zhaohua, and Norden E. Huang, “Ensemble empirical mode decomposition: a noise-assisted data analysis method,” Advances in Adaptive Data Analysis, vol. 1, no. 1, pp. 1-41, 2009.
［7］ Yeh, J.-R., J.-S. Shieh, and N. E. Huang, “Complementary ensemble empirical mode decomposition: A novel noise enhanced data analysis method,” Advances in Adaptive Data Analysis, vol. 2, no. 2, pp. 135-156, 2010.
［8］ Wang, Yung-Hung, Kun Hu, and Men-Tzung Lo, “Uniform phase empirical mode decomposition: An optimal hybridization of masking signal and ensemble approaches,” IEEE Access, vol. 6, pp. 34819-34833, 2018.
［9］ Colominas, Marcelo A., Gastón Schlotthauer, and María E. Torres, “Improved complete ensemble EMD: A suitable tool for biomedical signal processing,” Biomedical Signal Processing and Control, vol. 14, pp. 19-29, 2014.
［10］ Lin, L., and J. Hongbing, “Signal feature extraction based on an improved EMD method,” Measurement, vol. 42, no. 5, pp. 796-803, 2009.
［11］ Kerkeni, L., Serrestou, Y., Raoof, K., Mbarki, M., Mahjoub, M. A., and Cleder, C., “Automatic speech emotion recognition using an optimal combination of features based on EMD-TKEO,” Speech Communication, vol. 114, pp. 22-35, 2019.
［12］ Khaldi, K., Boudraa, A. O., Bouchikhi, A., and Alouane, M. T. H., “Speech enhancement via EMD,” EURASIP Journal on Advances in Signal Processing, pp. 1-8, 2008.
［13］ Chatlani, N., and Soraghan, J. J., “EMD-based filtering (EMDF) of low-frequency noise for speech enhancement,” IEEE Transactions on Audio, Speech, and Language Processing, vol. 20, no. 4, pp. 1158-1166, 2011.
［14］ Zão, L., Coelho, R., and Flandrin, P., “Speech enhancement with EMD and Hurst-based mode selection,” IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 22, no. 5, pp. 899-911, 2014.
［15］ Chang, N., T. Chen, C. Chiang, and L. Chen, “On-line empirical mode decomposition biomedical microprocessor for Hilbert Huang transform,” in Proceedings of the IEEE Conference on Biomedical Circuits and Systems, pp. 420-423, 2011.
［16］ Faltermeier, R., et al., “Weighted sliding empirical mode decomposition,” Advances in Adaptive Data Analysis, vol. 3, no. 4, pp. 509-526, 2011.
［17］ Faltermeier, R., A. Zeiler, I. R. Keck, A. M. Tomé, A. Brawanski, and E. W. Lang, “Sliding empirical mode decomposition,” in Proceedings of the International Joint Conference on Neural Networks, pp. 1-8, 2010.
［18］ Fontugne, R., P. Borgnat, and P. Flandrin, “Online empirical mode decomposition,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 4306-4310, 2017.
［19］ CY, C., & CMY, K. ITU-T Standards and Recommendations G.114.
［20］ Wang, Y. H., Liang, S. F., Kuo, T. B., and Lin, Y. C., “Software Implementation of Real-time EMD-based Algorithm in Embedded Microprocessors for Wearable Devices,” IEEE Transactions on Instrumentation and Measurement, 2024.
［21］ Wang, Y.-H., I.-Y. Chen, H. Chiueh, and S.-F. Liang, “A low-cost implementation of sample entropy in wearable embedded systems: An example of online analysis for sleep EEG,” IEEE Transactions on Instrumentation and Measurement, vol. 70, pp. 1-12,. 2021.
［22］ Hsieh, T.-H., M.-H. Liu, C.-E. Kuo, Y.-H. Wang, and S.-F. Liang, “Home use and real-time sleep-staging system based on eye masks and mobile devices with a deep learning model,” Journal of Medical and Biological Engineering, vol. 41, no. 5, pp. 659-668, 2021.