# Audio Steganalysis Estimation with the Goertzel Algorithm
## 3 Performance Evaluation
### Frequency Analysis Decomposition  
#### 3.4.1 Goertzel Algorithm for Frequency Scanning Audio Vectors  
For steps 2, 3, and 4, after separating the audio vector into left and right channels, we performed a frequency spectrum analysis using the Goertzel algorithm. The Goertzel algorithm was applied to each separated channel to obtain their frequency spectrums. The separated vectors preserved a standard sampling rate of 44,100 samples per second in wav audio files, with \(N=100\). Test 1. Audio files without attacks  
As a result, vectors corresponding to the frequency spectrums of the left and right channels of the original audio vectors were obtained, as shown in Figure 8a-f. Each resulting vector contains the magnitude of the information contained in the frequency components that conform to the audio vectors. Similarly, the [PERSON] algorithm was applied to possible stegoaudios. Figure 9a-f, shows the frequency spectrum of the channels of the possible stegoaudio vector. Figure 9: _Cont._Audio comparison original audio analysis Goertzel vs. stegoaudio analysis Goertzel. Subsequently, Figure 10 shows graphically the difference between the analysis of the original audio and the supposed stegoaudio. Figure 10: Cont. Figure 9: Graphics of the spectrum magnitudes of the left and right channels of the possible stegoaudio. (**a**) Magnitude spectrum of the left channel of the stegoaudio in analysis. (**b**) Magnitude spectrum of the right channel of the stegoaudio in analysis. (**c**) Magnitude spectrum of the left channel of the stegoaudio in analysis. (**d**) Magnitude spectrum of the right. (**e**) Magnitude spectrum of the left channel of the stegoaudio in analysis. (**f**) Magnitude spectrum of the right channel of the stegoaudio in analysis. From Figure 10a,c,e, we can see in the graphs the range of frequencies in red. These belong to the tones (fingerprints) that have been detected in the right channel of the audio vector as possible information not belonging to the original audio vector. We observe this in a similar way in Figure 10b,d,f; the graphs obtained from the analysis in the left channel are presented in red. From this analysis we conclude that there is information added to the audio vector. Test 2. Audio files with text and image files. Goertzel algorithm for frequency scanning audio vectors. As a result, the vectors corresponding to the frequency spectrums of the left and right channels of the original audio vectors were obtained, as shown in Figure 11a-f. Each resulting vector contains the magnitude of the information contained in the frequency components that conform to the audio vectors. Figure 11: Cont. Figure 10: Comparative graphic of the magnitude spectrum of the original audio channels and the possible stegoaudio. (**a**) Comparison of the magnitude spectrum of the left channel of the original audio and the possible stegoaudio in analysis. (**b**) Comparison of the magnitude spectrum of the right channel of the original audio and the possible stegoaudio in analysis. (**c**) Comparison of the magnitude spectrum of the left channel of the original audio and the possible stegoaudio in analysis. (**d**) Comparison of the magnitude spectrum of the right channel of the original audio and the possible stegoaudio in analysis. (**e**) Comparison of the magnitude spectrum of the left channel of the original audio and the possible stegoaudio in analysis. (**f**) Comparison of the magnitude spectrum of the right channel of the original audio and the possible stegoaudio in analysis. Stegoaudios. Similarly, the Goertzel algorithm was applied to the possible stegoaudios. Figure 12a-f, shows the frequency spectrum of the channels of the possible stegoaudio vector. From the graphs in Figure 11 related to the original audio vectors, we can see that the Goertzel algorithm did not detect any tone outside the frequency range of the vector (vector without information).