低記憶體需求及效能易縮放之經驗模態拆解及其硬體實現

Memory-Efficient & Scalable Empirical Mode Decomposition (EMD) and its Hardware Implementation

曾紀宇(Ji-Yu Tseng)

指導教授 ： 林泰吉

國立中正大學/工學院/資訊工程學系/碩士(2013年)

摘要

經驗模態分解（Empirical Mode Decomposition；EMD）已被證實在「非線性（non-linear）」與「非穩態（non-stationary）」的訊號分析中有著卓越的效果，但其運算量與耗用記憶體極大，故少見其應用在嵌入式即時訊號處理中。本論文針對EMD需求大量記憶體之立方雲線計算提出「分段式（segmented）立方雲線（cubic spline）計算」有效降低系統緩衝記憶體需求；另外對於分段式立方雲線中的兩組參數分段長度(n)及重疊點數(m)影響提出一套探索方法，並指出當其變化時對於系統整體處理能力、訊號品質、平行化程度及記憶體使用量的影響程度。最後本論文提出「適用於軟體與硬體的EMD平行計算架構」進一步地縮減其整體的計算時間。本論文所提出之「分段式立方雲線計算」、「分段系統參數探索方法」及「適於分段式立方雲線EMD平行計算架構」等最佳化設計均以FPGA完成驗證。並相對於原始EMD演算法中的立方雲線計算，本論文所提出之設計在處理長度2,048點並篩選10次時，可減少95.3%的記憶體使用量。

關鍵字

經驗模態分解硬體架構 ； 分段式立方雲線 ； 經驗模態分解

並列摘要

Empirical mode decomposition (EMD) has outstanding performance in non-linear and non-stationary signal analysis. But it is not widely adopted in embedded and real-time signal processing applications due to its high computing complexity and high memory requirement. This thesis proposes a memory-efficient EMD design with parallel architecture, which has been integrated into an embedded system successfully. First, a memory-efficient segmented cubic spline computation is proposed to reduce the memory requirements in EMD. Then, a systematic exploration is proposed for the segment size & overlapped points of the segmented cubic spline, which affect computing time, quality and memory sizes. Finally, a scalable hardware architecture is proposed for our memory-efficient EMD. The above design techniques have been implemented and verified using FPGA and a real-time processing system has been demonstrated. Compared with the original approach, our proposed algorithm can reduce 95.3% memory in spline computations for 2,048-points EMD.

並列關鍵字

Segmented cubic spline ； Empirical Mode Decomposition (EMD) ； EMD hardware architecture

參考文獻

[1] N. E. Huang, et al., “The empirical mode decomposition and the Hilbert spectrum for non-linear and non-stationary time series analysis,” in Proc. R. Soc. Lond., pp. 903-995, 1998.

[2] A. Zeiler, et al., “Empirical mode decomposition: an introduction,” in Proc. IJCNN, pp. 1-8, 2010.

[3] M. Blanco-Velasco, B. Weng and K. E. Barner, “ECG signal denoising and baseline wander correction based on the empirical mode decomposition,” Comput. Biol. Med., pp. 1-13, Jan. 2008.

[4] M. Blanco-Velasco, B. Weng, and K. E. Barner, “ECG signal denoising and baseline wander correction based on the empirical mode decomposition,”Comput. Biol. Med., pp. 1-13, Jan. 2008.

[6] R. R. Zhang, S. Ma and S. Hartzell, “Signatures of the seismic source in EMD-based characterization of the 1994 Northridge, California, earthquake recordings,” BSSA, vol. 93, no. 1, pp. 501-508, Feb. 2003.