# Audio Steganalysis Estimation with the Goertzel Algorithm
## 4 Statistical Coefficient Results  
To quantitatively evaluate the performance of the proposed steganalyzer, we obtained the higher-order statistical coefficients. We also added classic estimates of noise estimation metrics in various media, such as images or audio files, to these coefficients. The mean squared error (MSE) was the considered metric. The coefficients of the statistical high order considered for the comparison include the mean, the standard deviation, the variance, the asymmetry, and the kurtosis [26; 27]. As mentioned in Section 2, these coefficients allow us to identify the distinctive characteristics of the distribution of information and, in this case, of the compared audio vectors. The first coefficient of the high statistical order (mean) allows us to identify the average magnitude of the information in each analyzed vector. This value allows us to visualize the variation in the signal with respect to its central value. The standard deviation and variance show the differences between the remaining magnitudes and the obtained mean magnitude. In addition, the signal distortion measurement can be visualized. The skewness indicates in which direction there is a greater amount of information; the skewness value is positive when it is on the right (high frequencies) and negative on the left (low frequencies). Finally, kurtosis shows the concentration of the vector information in relation to the average, that is, if the information of the vector is more concentrated in the center or at the borders. Table 1 shows the obtained mean, skewness, variance, standard deviation, and kurtosis values. These results indicate small variations in the values obtained from the mean, standard deviation, variance, skewness, and kurtosis. For reasons of space, we added tests of only the 10 combinations examined, the stegoaudios modified, and differing values were obtained from the original audios, showing evidence that the frequency components of the audios have been modified. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Test**} & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Standard Deviation**} & \multicolumn{2}{c}{**Variance**} & \multicolumn{2}{c}{**Skewness**} & \multicolumn{2}{c}{**Kurtosis**} & \multicolumn{2}{c}{**Average Difference**} \\ \cline{2-11}  & **Left** & **Right** & **Left** & **Right** & **Left** & **Right** & **Left** & **Right** & **Left** & **Right** & **Left** & **Right** \\ \hline \multirow{2}{*}{1} & 0.1331 & 0.1412 & 0.1920 & 0.1962 & 0.0369 & 0.0385 & 2.0433 & 1.8591 & 6.9245 & 6.0740 & 1.8659 & 1.6618 \\  & 0.1383 & 0.1444 & 0.1941 & 0.1942 & 0.0377 & 0.0377 & 2.0488 & 1.8774 & 6.9224 & 6.1448 & 1.8682 & 1.6797 \\ \hline \multirow{2}{*}{2} & 0.1507 & 0.1309 & 0.2170 & 0.1860 & 0.0471 & 0.0346 & 1.7994 & 1.9302 & 5.5369 & 6.4662 & 1.5512 & 1.7495 \\  & 0.1565 & 0.1611 & 0.2158 & 0.1643 & 0.0466 & 0.0270 & 1.8125 & 2.0356 & 5.5893 & 6.8439 & 1.5641 & 1.8463 \\ \hline \multirow{2}{*}{3} & 0.1275 & 0.1313 & 0.1862 & 0.1766 & 0.0347 & 0.0312 & 2.1335 & 1.9504 & 7.4058 & 6.5890 & 1.9779 & 1.7757 \\  & 0.1335 & 0.1353 & 0.1816 & 0.1732 & 0.0330 & 0.0300 & 2.2027 & 2.0194 & 7.7986 & 6.9441 & 2. From Table 1, the numbers highlighted in bold are the values that denote that there is an alteration in the audio vectors. The obtained results reveal that information has been hidden inside the stegoaudios. From the results obtained we observe that the most affected vector is audio test #1. The insertion of this information modifies, in a similar way, all the host vectors based on the results obtained for the mean, standard deviation, variance, skewness and kurtosis. In each of the tests conducted on the pairs of vectors, variations are present that can be interpreted as a modification or alteration of the audio vectors using the results obtained.