# Method for Resonant Frequency Attenuation in Dynamic Audio Equalizer
## 2 Materials and Methods
### Filter Bank and Signal Filtering
The stability of the system was probed under the Nyquist frequency, taking into consideration the maximum operating frequency of 22,000 Hz. This frequency is below the minimum audio frequency of 22,050 Hz (with a minimum sampling frequency of 44,100 Hz). Furthermore, the filter exhibits instability when the attenuation value is below \(-600\) dBFS. To prevent this, the attenuation is constrained to a range of \(-145\) dBFS to 0 dBFS. The preceding considerations indicate that the system will be stable and that the input signal will be processed with minimal delay, as all poles and zeros of the filter section are located within the unit circle. Figure 11 illustrates the pole-zero diagram for the Table 1 case and the frequency response of Figure 9 presented in Section 2.4. The algorithm's performance was evaluated by developing it into an audio plug-in, enabling a direct comparison with the commercial plug-ins Soothe2 and RESO. The assessment was conducted using these plug-ins' default settings and their free trial versions. Twenty audio files from disparate sound sources were subjected to analysis and segmentation into five distinct groups. All these files can be found in the repository given at the end of this paper. The groups were designated as follows: percussion, guitars, wind instruments, other instruments, and voices. The dataset consists of twenty audio files that have been carefully selected to include a variety of instruments and conditions that are representative of real-life scenarios in commercial music applications. In particular, the selection includes versatile instruments in different conditions such as percussion with reverb, guitars in different scenarios such as acoustic, clean electric, distorted, and effects, vocals in different conditions, various wind instruments, and other instruments commonly used in commercial music such as the organ, piano, and electric bass. This diversity ensures that the dataset captures a wide range of acoustic characteristics. The metrics employed for analysis were the integrated RMS and LUFS levels measuring the attenuation of the processed audios. Attenuation by octave bands over time was obtained using the Wavelet transform. Finally, the inter-annotator agreement metric was implemented with 40 individuals from the audio field involved in order to ascertain whether the attenuation generated was at resonant frequencies. The level of experience of the annotators ranged from 2 to 10 years or more in different areas of audio and music. Audio engineers, producers, musicians, audiophiles, and music-related people were considered in the evaluation. The experience of the annotators was carefully considered in order to ensure the transparency of the results for the project. In the course of the experiment, participants were asked to listen to the original audio files and to the audio files processed by the proposed plug-in, using headphones. After listening to each audio file, the participants were asked the following questions:  
* Do you hear a difference between the output audio file and the input audio file? * Do you consider the difference you hear in the output file to be the attenuation of resonant frequencies in the input audio file? * Do you think the attenuation in the low/mid frequencies addresses the resonant frequencies of the input file? * Do you think the attenuation in the mid/high frequencies addresses the resonant frequencies of the input file? It should be noted that all four questions had only binary (yes/no) answers. From the responses, it was possible to average for each question how many people answered yes and how many answered no, thus analysing the responses across the spectrum and in low- and high-frequency sections. In general, the developed plug-in exhibits higher attenuation than commercial plug-ins. As shown in Table 2, the attenuation is \(-2.32\) dB in RMS and \(-2.33\) in Integrated LUFS. In contrast, Soothe2 has an attenuation of \(-1.27\) dB in RMS and \(-1.28\) Integrated LUFS.