# A Novel Wavelet-Based Algorithm for Detection of QRS Complex
## 4 Results and Discussion
### Illustrations of the Identifications of QRS Peaks
Based on the evaluation of the sharpness of P1 and P2 using Equation (9), P2 is identified as not a QRS peak because the sharpness parameter of P1 is larger than that of P2. The identification of P3 is Case 2.2 in Section 3.7 because the distance between P1 and P3 is 126 samples, is greater than 100 samples, and is less than 130 samples. It is obvious that the current candidate QRS peak, P3, has no extremum pair  
Figure 10: Illustration of the identifications of QRS peaks for Case 2.1. Figure 9: Illustration of the identifications of QRS peaks for Case 1.  
in the higher frequency d2', but the previous QRS peak, P1, has one. Hence, P3 is identified as not a QRS peak. It is considered as a T-peak. Performance Evaluation of the Proposed QRS Peak Detection System and Comparison with the Previous Studies  
The MIT-BIH arrhythmia database containing 48 ECG recordings was used to evaluate the performance of the proposed QRS peak detection system in order to compare with some previous specific studies which used the same database. An identified QRS peak is recorded as a true peak if it is located within 100 ms (i.e., 36 samples at sampling rate of 360 Hz) of the annotation time [12]. The commonly used performance parameters for the QRS peak detection system are defined as follows:  
Sensitivity (Se):  
\[\text{Se}(\%)=\frac{\text{TP}}{\text{TP}+\text{FN}}\times 100\% \tag{10}\]  
Positive prediction value (+P):  
\[+\text{P}(\%)=\frac{\text{TP}}{\text{TP}+\text{FP}}\times 100\% \tag{11}\]  
Detection error rate (DER):  
\[\text{DER}(\%)=\frac{\text{FP}+\text{FN}}{\text{Total No. of QRS Beats}}\times 100\% \tag{12}\]  
where TP is the number of true positive peaks (QRS peaks detected as QRS peaks), FN is the number of false negative peaks (QRS peaks detected as Not QRS peaks), and FP is the number of false positive peaks (Not QRS peaks detected as QRS peaks). Table 1 lists the summary performance of the proposed QRS detection algorithm using the first channel of the MIT-BIH arrhythmia database. Most of the QRS peaks can be accurately detected by the proposed algorithm even if the ECG signals include severe baseline drifts, abrupt changes, high-frequency noise, low-amplitude QRS complexes, sharp P and T waves, or wide ventricular premature contractions. There are a total of 271 detection failures including 180 false negative beats and 91 false positive beats. The highest number of detection failures is 46 failures for recording 203,  
Figure 11: Illustration of the identifications of QRS peaks for Case 2.2 and Case 3. Table 2 shows the performance comparison of the proposed QRS peak detection system with the previous studies. In addition to [PERSON] et al. [14] only providing the results of one-minute signal per ECG recording, other studies have the results of complete 30-minute signal per ECG recording. Though the FN and FP of [PERSON] et al. [14] have only 22 and 26, respectively, its DER of 1.49% is the highest among the studies in Table 2. Comparing the proposed algorithm with wavelet-based methods using 30-minute ECG signals, the minimum FN is 140 for [PERSON] et al. [19], followed by 178 for [PERSON] et al. [12] and 180 for the proposed algorithm, and the proposed method has the minimum FP of 91 and FP+FN of 271. The proposed algorithm has the best DER of 0.25% and +P of 99.92% among the wavelet-based methods in Table 2. The Se of the proposed method is 99.84%, which is slightly lower than 99.87% of [PERSON] et al. [14]. The results show that the proposed method improves the QRS detection accuracy of the wavelet-based methods. Most of the previous studies removed the high-frequency noise to increase the signal-to-noise ratio and reduce the interference of noise. However, the pre-filtering out of the high-frequency components would not only reduce the noise level, but also cause a reduction in the amplitudes of the QRS peaks and a decrease in the detection accuracy of the QRS peaks.