## 4 Experimental Results
### Experiments on Mono Audio  
We used seven audio clips belonging to seven different genres as host audio signals to illustrate the performance of our watermarking algorithm on mono-channel audio. They were \"Drama,\" \"Debate,\" \"Sports Commentary,\" \"Classical Music,\" \"Jazz Music,\" \"Pop Music,\" and \"Rock Music.\" All audio files were in the WAVE format, mono, sampled at 48 kHz, quantized with 16 bits, and 30 s long. The scale factor \(\xi_{i}\) was adaptively adjusted by CSNR, as we mentioned in Section 3.1. Here, we first showed CSNR with 24 kbps HE-AAC v1 compression for two test audios and the sum of CSNR histograms of all seven test audio signals in Figure 8. From the histogram graph, we can see that most CSNR values were distributed from 0 to 15. According to the histogram distribution, we found that calculating \(\xi_{i}\) by following Equation (11) well balanced the trade-off between robustness and imperceptibility in our implementation. \[\xi_{i}=\left\{ \begin{array}{cc}0.2,&14\leq CSNR_{i}\\ -0.05\text{-}CSNR_{i}+0.9,&0\leq CSNR_{i}<14\\ 0.9,&CSNR_{i}<0\end{array} \right. \tag{11}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Impairment Description** & **ODG** & **Quality** \\ \hline Imperceptible & 0.0 & Excellent \\ Perceptible, but not annoying & \(-1.0\) & Good \\ Slightly annoying & \(-2.0\) & Fair \\ Annoying & \(-3.0\) & Poor \\ Very annoying & \(-4.0\) & Bad \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Objective difference grades (ODG) for audio quality evaluations. The data payload refers to the number of bits that can be embedded into the audio signal within a unit of time and is measured in the unit of bps (bits per second). The data payload of our algorithm was determined by frame length \(T_{f}\), where one bit watermark is embedded. For example, if \(T_{f}=500\) and the sampling rate of the host audio is 48,000 Hz, we can embed 48,000/500 = 96 bits per second in the audio. As the frame length will affect the imperceptibility and robustness of our algorithm, in Table 2 and Figure 9, we show how the change of data payload influenced ODG and BER, where BER was calculated after the HE-AAC v1 24 kbps compression. From the table and graph, we can see that BER was under 2% when the data payload was lower than 96, but it riose rapidly from 1.77 to 8.77% when the data payload was 96-192 bps (\(T_{f}=250\)). With the increase of data payload, the ODG was slightly increased and larger than \(-1\), which indicates the original and watermarked audio signals were perceptually similar and not annoying. Besides the frame length, the other important parameter of the proposed algorithm is passband frequency. If the selected passband frequency is too low or too high, it is likely to yield bad results for BER, as the audio compression will remove most of signals in that frequency range based on the psychoacoustic model. Moreover, HE-AAC applies SBR to directly cutoff high frequencies, which will result in worse BER results. Table 3 and Figure 10 show how the selected passband frequency influences the ODG and BER, where BER was calculated after the HE-AAC v1 24 kbps compression. As shown in the table and graph, we observed that, when using a frequency higher than 3.5 kHz, BER was over 5% and rose rapidly. When using a passband frequency of 0.5-3.5 kHz, the ODG was lower than \(-1\), the other frequency ranges were all larger than \(-1\), and the BER was also worse than when using 1.5-4.5 kHz and 2.5-5.5 kHz. Therefore, we can conclude that the 1.5-5.5 kHz frequency range is a good choice for embedding watermarks with the proposed algorithm. Note that this range of frequency bands is very sensitive to the human hearing system according to the absolute threshold of hearing. Almost all audio watermarking methods were designed to avoid this range of frequency to meet the imperceptibility requirement, though our method achieved high imperceptibility on the 1.5-5.5 kHz frequency band while maintaining a low BER. Figure 8: Calculated CSNR of test audio (**a**) CSNR of “Sports Commentary” audio.