# Audio Steganalysis Estimation with the Goertzel Algorithm
## 6 Conclusions  
In this work, we present the Goertzel algorithm as an alternative means of detecting possible attacks on audio signals. The tests were carried out with audio signals and were divided into two blocks. Other audio signals were inserted into the first block through steganographic tools known as STEGHIDE. A qualitative analysis was applied to these tests, showing graphs of the audio \begin{table}
\begin{tabular}{c c} \hline
**Test** & **Time Processing (s)** \\ \hline
1 & 0.265 \\
2 & 0.422 \\
3 & 0.262 \\
4 & 0.257 \\
5 & 0.251 \\
6 & 0.257 \\
7 & 0.254 \\
8 & 0.275 \\
9 & 0.251 \\
10 & 0.294 \\ \hline \end{tabular}
\end{table} 
Table 13: Comparative table of methods in the literature against the proposed method. \begin{table}
\begin{tabular}{c c c} \hline
**Stegoanalysis Method** & **Steganography Method** & **HIT** \\ \hline Proposed in [25] & LSFQ & 95.97\% \\ Proposed in [38] & Steghide & 90–98\% \\  & MIN & 99.90\% \\ Proposed in [39] & SING & 99.87\% \\  & HCM & 99.50\% \\ Proposed in [5] & S-tools & 99.55\% \\  & Hide4 PGP & 98.3\% \\ Proposed in [12] & \multicolumn{2}{c}{\(\qquad\signals obtained from the Goertzel analysis. The original audio signals, attacked audio signals and audio signals are displayed, and audio signals processed using the Goertzel algorithm are also obtained. Visually, it is observed that there is a marked difference between the audio signal without audio insertion vs. the audio signal with inserted audio, which represents that the audio file was attacked. Similarly, for test block 2, other types of signals were added, such as plain text and images, to confirm that the proposal is robust for any type of data inserted. Qualitative results were obtained in which the difference between the original audio signal and the possible stegoaudio was visibly shown, from the difference signals, it was visibly observed that the signal had been attacked by external data. To reinforce this analysis, the AQM analysis is also implemented, where the performance applying the Goertzel algorithm for the detection of stegoaudios exceeds almost double the performance results obtained from the files that were not processed. Quantitatively, the analysis was carried out using AQM metrics, which were proposed as an analysis mechanism in time and frequency in order to find the differences in the signals in these domains. From the results obtained, we observed that the performance in detection it increased twice as compared to the signals that were not processed by Goertzel. In both tests carried out for both the audio vectors attacked with audio and for the audio vectors attacked with images and text, a result of 100% abnormality detection was obtained by applying Goertzel. Unlike the tests that were not performed by Goertzel, performance results of less than 50% were obtained. Comparisons were made with other state-of-the-art steganalyzers, showing a performance of 100% compared to methods that implement convolutional neural networks, which present a performance between 91% and 99.90%. The processing times of each test were obtained, obtaining results of less than 0.5 s. Finally, we demonstrate that the Goertzel algorithm is a powerful tool for the detection of signals that can possibly be stegoaudios with a computational cost of less than 0.5 s. It is shown that this algorithm was designed for the detection of tones or changes in the intensities of audio signals during the frequency sweep. As a future work, hybrid models can be created by applying the Goertzel algorithm. The results obtained show that it is also invariant to audio, text or image signals, providing a larger field of study for frequency analysis. B.E.C.-G.: conceptualization, analysis, investigation, supervision, project administration, and funding acquisition; M.A.C.-M.: analysis, validation, and investigation; L.A.C.-B. : analysis and validation; F.J.G.-F.: review and editing; and M.A.D.-C.: analysis and investigation. All authors have read and agreed to the published version of the manuscript.