# Method for Resonant Frequency Attenuation in Dynamic Audio Equalizer
## 2 Materials and Methods
### Filter Bank and Signal Filtering
RESO exhibits an attenuation of \(-1.1\) dB in RMS and \(-1.08\) Integrated LUFS. The present study employs a statistical approach based on octave bands and by groups of audio files instead of analyzing specific resonant frequencies in each piece of audio. This method allows more general conclusions to be drawn about the effectiveness of the system in the proposed groups while avoiding biases caused by individual cases. The octave band analysis revealed that, in terms of attenuation, the audio plug-in generally coincided with the other two plug-ins in the 31.25 Hz band and from 500 Hz to 4 kHz. There was a notable degree of agreement between the present work and Soothe2, with both 125 Hz and 8 kHz exhibiting attenuation greater than \(-0.1\) dB, as illustrated in Table 3 and Figure 12.  
In the analysis of the annotator agreement, 74% of the population indicated that attenuation occurs at the resonant frequencies throughout the spectrum. Additionally, 59% of respondents agreed that attenuation in low frequencies occurs at the resonances, while 60% of respondents agreed that attenuation of high frequencies occurs at the resonances in that section. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Metric** & **Current Plug-In** & **Soothe2** & **RESO** \\ \hline Mean RMS [dBFS] & \(-2.32\pm 1.08\) & \(-1.27\pm 0.92\) & \(-1.10\pm 1.17\) \\ Mean LUFS 1 [LUFS] & \(-2.33\pm 0.99\) & \(-1.28\pm 0.94\) & \(-1.08\pm 1.08\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RMS and Integrated LUFS values for the three analyzed plug-ins. Figure 11: Unit circle in the \(Z\)-plane with poles and zeros at a specific time of the proposed system for audio from a drum set. Additionally, each group of audio files was analyzed by octave bands. The group where there is a general agreement between the three plug-ins is the voice group. In this group, the three plug-ins agree at 31.25 Hz and from 500 Hz to 4 kHz with attenuation between \(-2.5\) dB and \(-1\) dB. With Soothe2, the agreement extends from 31.25 Hz to 8 kHz. The Figure 13 illustrates that the three plug-ins generate comparable attenuation. It can be confirmed that the attenuation occurs over the resonant frequencies, as evidenced by the 83.75% of respondents who indicated that the attenuation occurs over the resonant frequencies in the annotator agreement. Additionally, 66.25% of respondents indicated that the attenuation occurs over high frequencies coinciding with the resonant frequencies. These frequencies are crucial because they contain the highest harmonic content of voices. Figure 12: General attenuation curves by octave bands for three plug-ins. \begin{table}
\begin{tabular}{l c c c} \hline \multirow{2}{*}{**Frequency**} & **Current Plug-In** & \multirow{2}{*}{**Soothe2 [dBFS]**} & \multirow{2}{*}{**RESO [dBFS]**} \\  & [dBFS] & & \\ \hline
31.25 Hz & \(-0.52\pm 0.48\) & \(-0.11\pm 0.16\) & \(-0.10\pm 0.23\) \\
62.5 Hz & \(-0.60\pm 0.39\) & \(-0.06\pm 0.11\) & \(-0.06\pm 0.10\) \\
125 Hz & \(-0.90\pm 0.63\) & \(-0.10\pm 0.11\) & \(-0.03\pm 0.07\) \\
250 Hz & \(-1.06\pm 0.78\) & \(-0.23\pm 0.23\) & \(-0.02\pm 0.05\) \\
500 Hz & \(-1.67\pm 1.51\) & \(-0.66\pm 0.63\) & \(-1.03\pm 1.96\) \\
1 kHz & \(-2.01\pm 1.42\) & \(-0.78\pm 0.85\) & \(-1.07\pm 1.25\) \\
2 kHz & \(-1.98\pm 0.97\) & \(-0.73\pm 0.62\) & \(-1.34\pm 1.20\) \\
4 kHz & \(-1.79\pm 1.01\) & \(-0.73\pm 0.84\) & \(-0.45\pm 0.55\) \\
8 kHz & \(-1.32\pm 1.20\) & \(-0.22\pm 0.27\) & \(-0.08\pm 0.14\) \\
16 kHz & \(-0.57\pm 0.67\) & \(-0.06\pm 0.08\) & \(-0.07\pm 0.19\) \\ \hline \end{tabular}
\end{table} 
Table 3: Average attenuation per octave band of all audio files in dBFS. The developed plug-in exhibits greater attenuation than the other two in the percussion and guitar groups.