根據衛生署公布的數據來看，心臟疾病位居台灣前十大死因的第二名，因此越來越受人們的重視，而心電圖訊號是最常用來診斷心臟疾病的依據，為了能長時間的紀錄和監控病人狀態，可攜式的量測儀器已成為現在發展的主流，可攜式量測儀器的發展除了要注意體積小和低功耗以外，對於雜訊的處理也是重要的課題。

本論文主要包含了兩個主題，一個為去除量測中因為移動或是任何外在因素所造成的雜訊，另一個為R波的偵測讓我們能夠精確計算心跳速率。選擇的方法為小波分析，小波分析的特性為可同時得到時間和頻率兩種狀態下的結果，近年來的應用常被用來消除雜訊。我們先利用不同種類的小波轉換及不同的thresholding方法去做雜訊的分析，根據得到的結果決定使用Symlets wavelets中的sym5為母波以及結合soft thresholding來做第一階段的去雜訊，之後將處理完的訊號根據頻段，選擇合適的層級作後續R波的尋找，最後再利用R波的位置進行第二次的去雜訊動作。

本論文提出的演算法利用MIT心律不整資料庫來驗證，錯誤率為0.65%。 對於消除肌電訊號造成的干擾的部分，在訊雜比為5dB的狀態下，使用我們所提出的演算法進行去雜訊動作後，訊雜比的改善量可以達到10dB以上。而將提出來的演算法，對實際量測到的心電圖訊號進行分析，針對R波的部分，在運動速度9km/hr以下，不論是走路跑步或是上下樓梯，R波能夠精確判斷。由此看來，我們所提出的演算法可以正確的找出R波，並能有效的清除雜訊，讓心電圖訊號能有更正確的解讀。

According to the data released by the Department of Health, Executive Yuan of Taiwan the heart disease was ranked number two among the top ten causes of death in Taiwan. Therefore, people pay more attention to heart disease now. The electrocardiogram (ECG) signal is the most commonly used condition to diagnose the heart disease. For long-term monitoring, the portable measuring instruments have become the mainstream. In addition to focus on the small size and low power of the development of portable measuring instruments, noise reduction is also an important topic.

In this thesis, there are two main research topics about ECG signal proposed. One is noise reduction, and the other is R peaks detection. Both of the two algorithms are based on discrete wavelet transform (DWT). Wavelet transform (WT) is popular for signal processing recently which can supply time-frequency analysis. Thus, WT is efficient for analyzing non-stationary signals like ECG signal. Different bases, three thresholding algorithms and two kinds of wavelet transform are used to solve different kinds of noises in order to find the proper method of noise reduction. The signal-to-noise ratio (SNR) is used to evaluate the result. From the simulation results, the Symlets wavelets (sym5) and soft-thresholding are chosen as the wavelet function and thresholding method, respectively. Employ them to do noise correction at the first denoised stage. The second stage is R wave detection. The MIT-BIH arrhythmia database, the sampling rate is 360Hz, is used for example. As for QRS complex characteristics, the frequency range is from 5 to 40 Hz. Thus, we chose to reconstruct the decomposition level 3 to 5, because the frequency range of which is from 5.6 to 45 Hz. Choosing the adaptive threshold and window size is the key point for the result of error rate. Using two thresholds method leads to better performance, compared to using one threshold method. At the last stage, does noise correction again. In terms of R wave positions, the novel method is proposed for eliminating the electromyogram (EMG) signal.

MIT-BIH arrhythmia database is utilized to verify our simulation results for R wave detection. The algorithm for R wave detecion has a sensitivity of 99.70% and a positive predictivity of 99.65%. The error rate is 0.65% under all kinds of situation (0.37% if ignoring 3 worst cases). For noise correction, the improvement SNR is achieved at least 9.5dB at SNR 5dB, and most of the improvement SNR are better than other methods at least 1dB. To apply presented algorithms for the portable ECG device, all R peaks can be detected no matter when people walk, run or go up and down stairs below 9km/hr. Thus, the proposed method can identify R wave correctly and reduce the noise effectively, so that the diagnosis of heart disease can be more accurate.

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