心電圖(Electrocardiography, ECG)是用於偵測心臟電訊號的一種工具，目前被廣泛的應用在醫學上，如醫生可以使用ECG判斷患者心臟電生理系統的功能。在急救方面，自動體外去顫器會對致命性心律的患者除顫。但往往所取得ECG訊號時容易參雜著基線飄移、肌電訊號、市電干擾(Power-Line Interference, PLI)等雜訊，若診斷前未消除雜訊，將使醫生或儀器誤判，為此有許多學者在數位端使用自適應性濾波器來抑制ECG中的各種雜訊，在本篇論文將只探討PLI雜訊。自適應性濾波器有許多演算法，其中以最小均方濾波器(Least Mean Square, LMS)最廣為使用。在初始分析中指出，所有基於LMS的演算法皆具有消除PLI的能力，但在均方根誤差(Mean Square Error, MSE)卻發現濾波後訊號與原始ECG產生了極大的誤差。
　　本論文首先提出頻率域正規化最小均方濾波器演算法(FFT NLMS)，該演算法具備正規化最小均方濾波器(NLMS)與頻率域最小均方濾波器(FFT LMS)的優勢，既能對特定頻率調整追蹤，也可以動態調整步階以加速收斂，提升雜訊抑制能力。接著在透過FPGA與ARM共同運算平台實現FFT NLMS演算法，開發一個具即時性的市電干擾消除器。首先透過FPGA端實現一個1D-to-2D 架構且轉換長度為12點的FFT(Radix-3 × Radix-4)，透過此數位電路將時頻域訊號轉換。在所提出的FFT演算法中，僅需要使用94個複數加法即可完成所有運算，相較於zero-padding的16點FFT技巧(32個複數乘法、64複數加法)，可大幅減少計算量。接著轉換完的頻域訊號再透過AXI介面傳送至ARM端，ARM端接收到頻域訊號後即可執行FFT NLMS演算法以抑制PLI雜訊。
　　在經過數萬次的模擬與比對後得知，FFT NLMS對60Hz的PLI抑制能力與NLMS表現略勝，在MSE效能評比上，相對其他演算法如：FFT LMS與LMS，本論文所提出的演算法可分別有18與20dB的優異差距。透過心率變異度(Heart Rate Variability, HRV)的計算結果顯示，原始訊號經過60Hz的干擾再由FFT NLMS進行雜訊消除，亦能獲得最接近原始ECG的HRV。故FFT NLMS在ECG訊號還原度相較其他演算法更為接近，後續醫生或儀器在進行分析才能獲得更加精確的分析。

Electrocardiography (ECG) has been widely used in medicine for the detection of the electrical signal of cardiac. For example: the doctors can diagnose the cardiac diseases via the electrical conduction system of ECG. For first aid and emergency medical help, automated external defibrillator (AED) is applied to automatically diagnose the life-threatening cardiac arrhythmias of ventricular fibrillation and is able to treat them through defibrillation if the patient’s cardiac rhythm is fatal ventricular arrhythmia. However, several noises, such as baseline wander, muscle artifact, and power-line interference (PLI), are also mixed within ECG signal. Removing these noises before diagnosis plays the most important key. Many researchers proposed the Least Mean Square (LMS)-based adaptive filtering algorithm to reduce these noises. In the proposed simulation results, it revealed that all of the LMS-based algorithms would have the capability to reduce the PLI noise, but caused higher errors in Mean Square Error (MSE), which is a kind of signal quality criterial.
This paper proposed the transfer-domain (TD) adaptive filtering algorithm called FFT-based Normalized Least Mean Square (FFT NLMS). It combined the advantage of Normalized Least Mean Square (NLMS) and TD Least Mean Square (i.e. FFT LMS). The FFT NLMS not only can tack a specific frequency signal but also can adjust the step size to improve the convergence time. For hardware implementation, we adopt a FPGA and ARM co-operation platform for FFT NLMS to realize a real-time PLI canceler. The PLI cancelling process can be divided into three steps: 1) time domain signals are first transferred to frequency domain signals via a 1D-to-2D structure of 12-point FFT operation (i.e. Radix-3 × Radix-4) in FPGA. Compared with the 16-point Cooley-Tukey FFT with 4-point zero padding scheme (totally takes 32 complex multiplications and 64 complex additions), the proposed 12-point FFT only requires 94 complex additions. The result shows that it greatly reduces a lot of computational complexity. 2) the frequency domain signals converted from the proposed FFT processor are further transferred to ARM through AXI bus from FPGA. 3) ARM processor executes FFT NLMS to eliminate the PLI noise in ECG signal and remove the noise.
　　After tens of thousands of simulations and comparisons, the results demonstrate that the proposed FFT NLMS has better performance than NLMS in suppression capability of PLI in spectrum. For the comparison of MSE, FFT NLMS has the lowest error, which can reduce 18 dB and 20 dB less than FFT LMS, and LMS, respectively. Because the signal after FFT NLMS noise suppression (i.e. the reconstructed signal) is highly closed to the original ECG, the Heart Rate Variability (HRV) analytic result of the reconstructed signal is quite similar to that of original ECG signal. This implies that the proposed FFT NLMS algorithm has higher suppression capability and higher computational accuracy so that it would be very useful and helpful for future applications.

論文審定書 i
論文公開授權書 ii
誌謝 iii
摘要 iv
ABSTRACT vi
目錄 viii
圖次 xi
表次 xvi
第1章 緒論 1
1.1 研究背景 1
1.2 研究動機 3
1.3 研究目的 5
第2章 文獻探討 6
2.1 心電訊號 6
2.2 心電訊號擷取系統 9
2.3 數位濾波器 12
2.4 自適應性濾波器 15
2.4.1 最小均方濾波器 17
2.4.2 正規化最小均方濾波器 22
2.4.3 Error Based LMS 23
2.4.4 頻率域最小均方濾波器 24
第3章 研究方法 27
3.1 頻率域正規化最小均方濾波器 29
3.2 應用於心電訊號之市電干擾消除器 30
3.2.1 FPGA FFT電路實現 32
3.2.1.1 1D-to-2D 快速傅立葉轉換演算法 34
3.2.1.2 12點1D-to-2D FFT架構 36
3.2.1.3 Radix-3架構 37
3.2.1.4 Radix-4架構 37
3.2.1.5 轉換因子TF運算優化 38
3.2.1.6 Sin(2π/3)乘法優化 39
3.2.1.7 FPGA實現1D-to-2D FFT(Radix-3 × Radix-4) 40
3.2.2 ARM FFT NLMS演算法實現 43
3.2.3 FPGA與PLI Canceller交握資訊 46
3.2.4 Data Encoding與Data Decoding 48
第4章 研究結果 51
4.1 演算法效能比較 51
4.1.1 模擬I 51
4.1.2 模擬II 55
4.1.3 模擬III 58
4.1.4 模擬IV 61
4.1.5 學習曲線 67
4.1.6 心率變異度 72
4.2 硬體實現效能比較 77
4.2.1 實現結果I 77
4.2.2 實現結果II 80
4.3 計算複雜度比較 83
第5章 總結與未來展望 86
第6章 參考文獻 89
第7章 附件 95
7.1 HRV分析結果I 95
7.2 HRV分析結果II 98
7.3 模擬V-65 Hz PLI 01
7.4 模擬VI-57.5 Hz PLI 102
7.5 模擬VII-混合頻率PLI 104
7.6 模擬VIII-混合頻率PLI 105

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