# Adaptive and Blind Audio Watermarking Algorithm Based on Chaotic Encryption in Hybrid Domain
## 4 Experimental Results and Analysis
### Robustness  
Robustness is an important index for evaluating the watermarking algorithm performance. This study examines BER and NC to evaluate the robustness of this algorithm. There are several types of attacks applied to the watermarked audio signal:  
1. Gaussian noise: add 20 dB Gaussian noise. 2. Gaussian noise: add 30 dB Gaussian noise. 3. Gaussian noise: add 35 dB Gaussian noise. 4. Amplitude scaling: reduce the amplitude of the watermark audio signal to 0.8. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Indexes** & **Proposed** & **[1]** & **[4]** & **[10]** & **[18]** & **[25]** \\ \hline SNR (dB) & 24.58 & N/ A & 23.49 & 21.37 & 18.42 & 20.32 \\ Capacity(pps) & 172.27 & 125 & 172.27 & 43.07 & 172.27 & 139.97 \\ NC & 1 & / & 1 & / & / & / \\ BER (\%) & 0.00 & 0.00 & 0.00 & / & / & 0.12 \\ \hline \hline \end{tabular} Note that: / indicates no relevant datas are found in the selected literatures.  
\end{table} 
Table 1: Average experimental results about capacity and imperceptibility (without attack). Figure 5: Waveform comparison charts of an audio clip: (**a**) original audio clip; (**b**) watermarked audio clip. Figure 6: Spectrogram comparison charts of an audio clip: (**a**) original audio clip; (**b**) watermarked audio clip. * Amplitude scaling: amplify the amplitude of the watermark audio signal to 1.2. * Low-pass filtering: apply low-pass filter with 4 kHz. * MP3 compression: apply MP3 compression with 64 kbps. * MP3 compression: apply MP3 compression with 128 kbps. * echo interference: add an echo with 50 ms delay and 5% decay. * Resampling: change the sampling rates by 44100-22050-44100 Hz. * Requantization: change the quantization bits by 16-8-16 bits per sample. Figures 7-9 show that the extracted pictures are very similar to the original pictures shown in Figure 4 when resisting various attacks except for the Gaussian noise with 20 dB, which indicates the strong robustness of this proposed algorithm. The average results for NC are shown in Table 2. The similarity between the extracted pictures and original pictures reaches over 0.98 under various attacks, which shows the strong robustness. According to the experimental results for BER listed in Table 3, the following conclusions can be drawn:  
1. This adaptive algorithm has an excellent robustness against Gaussian noise, resampling, requantization, echo interference, MP3 compression and amplitude scaling, so it is far superior to the algorithms proposed in [1; 4; 10; 18]. This can be seen by comparing the results in column 2 and column 4 that the robustness of this adaptive algorithm is much better than that in [4], mainly because the embedding depth of each audio segment is adaptively controlled by the overall average amplitude. 2. The BER of this algorithm in resisting the low-pass filter is only 0.01%, which is higher than 0.39% in [1], 21.975% in [10], 28.250% in [18], and 0.12% in [25]. The average BER in case of Gaussian noise with 20 dB is 1.92%, which is inferior to the algorithm in [25], so some watermark bits may be lost when resisting strong noise attacks. The 4 th level wavelet coefficients will be affected by strong noise so as to reduce the robustness because this algorithm conceals the watermarks by modifying the 4 th-level coefficients. As the noise becomes smaller, BER are significantly declined in 30 dB and 35 dB. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Attack** & **The First Picture** & **The Second Picture** & **The Third Picture** & **Average Values** \\ \hline (1) & 0.9852 & 0.9881 & 0.9672 & 0.9802 \\ (2) & 0.9985 & 0.9989 & 0.9971 & 0.9981 \\ (3) & 0.9996 & 0.9998 & 0.9991 & 0.9995 \\ (4) & 1 & 1 & 1 & 1 \\ (5) & 1 & 1 & 1 & 1 \\ (6) & 1 & 1 & 1 & 1 \\ (7) & 0.9998 & 0.9997 & 0.9996 & 0.9997 \\ (8) & 1 & 1 & 1 & 1 \\ (9) & 1 & 1 & 1 & 1 \\ (10) & 1 & 1 & 1 & 1 \\ (11) & 0.9986 & 0.9992 & 0.9993 & 0.9990 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average results for normalized correlation (NC) under various attacks.