## 4 Evaluation
### Robustness Testing under Fixed SNR  
After the embedding process, some common attacks are applied to test the robustness, which will be measured by the bit error rate (BER). The BER, that is the ratio of bit errors to the total transferred errors during a tested time interval, is usually expressed as a percentage and can be formulated as:  
\[\text{BER}=\frac{B_{error}}{B_{total}}\times 100\% \tag{17}\]  
where \(B_{error}\) and \(B_{total}\) denote the numbers of error binary bits and total binary bits during a tested period. In general, the performance of a watermarking system is analyzed in terms of SNR and BER. However, there is a tradeoff between them. Accordingly, we compare our results with reference [10] which used a spread-spectrum technique under the same SNR = 32 dB conditions. In order to maintain the consistency of the watermarked signal and the original signal to the maximum extent possible since the insertion of the watermark will affect the original ECG signal, we use the formula in Equation (9) to obtain the proper embedding strength \(T\) = 4,000. Figure 6a shows that the original and watermarkedsignals for data set ID 100 look almost indistinguishable. Here the blue curve represents the original ECG signals; and the green curve represents the watermarked ECG signals. We enlarge the portion in Figure 6a and b around the first second and plot both on the same graph as drawn in Figure 6c which indicates that the difference before and after watermarked signals is almost negligible in the time domain.  
The results of testing three attacks are discussed in the following section:  
(1) _Noise corruption_: Since the ECG data may be transferred using a network, we first consider the white noise attack to test the robustness, i.e., \(S_{i}^{*}=\widetilde{\mathbf{S}}_{i}+\alpha\bullet y_{i}\) where \(\left\{\widetilde{\mathbf{S}}_{i}^{\prime}\right\}\) is the watermarked signal and \(\left\{S_{i}^{*}\right\}\) is the attacked signal which is influenced by the white noise \(\left\{y_{i}\right\}\) with zero mean and standard deviation one. Here \(\alpha\) is considered as the strength of the white noise, i.e., \(\left\{\alpha y_{i}\right\}\) is zero-mean white noise with standard deviation \(\alpha\). Table 1 describes the robustness of the watermarked ECG signal under white noise attack with different standard deviations.  
(2) _Low-pass filtering_: Table 2 shows the effect of using a low-pass filter with a cutoff frequency of 90, 100 or 140 Hz. The proposed method has lower robustness against the low-pass filter attack than the reference [10] at 90 and 100 Hz.  
Figure 6: The original and watermarked ECG. (**a**) Watermarked signal (**b**) Original signal; (**c**) Waveform comparison between 0.09 and 1.09 (s).  
3. _Re-sampling_: The sampling rate of the watermarked ECG signals was down-sampled from 360 Hz to 180 Hz and then back to 360 Hz using interpolation. Besides, we also adjust the sampling rate from 360 Hz to 90 Hz, 45 Hz, respectively, and then back to 360 Hz. Table 3 shows the results of these re-sampling processes, which indicate that the proposed scheme is more robust than that described in reference [10].