# Designing Audio Equalization Filters by Deep Neural Networks
## 5 Experiments  
The performance of the proposed and the baseline methods have been assessed by computer experiments using impulse responses measured inside real car cabins. Two car models have been considered, an Alfa Romeo Giulia and a Jeep Renegade. The Giulia was first taken for binaural equalization experiments (\(\mathcal{M}=2\)). The impulse responses were obtained using the sine sweep method [34] as implemented by the Aurora plugins ([[http://pcfarina.eng.unipr.it/Aurora_XP/index.htm](http://pcfarina.eng.unipr.it/Aurora_XP/index.htm)]([http://pcfarina.eng.unipr.it/Aurora_XP/index.htm](http://pcfarina.eng.unipr.it/Aurora_XP/index.htm))). Sampling was done at 28.8 kHz with a Roland Octa-Capture audio interface, then the impulse responses were resampled to 48 kHz. A Kemar 45 BA mannequin was placed on the driver's seat; the distance between its ears is \(d=18\) cm. The Giulia provides \(\mathcal{S}=7\) loudspeakers--four door woofers, one subwoofer in the trunk, one speaker in the center of the dashboard and one speaker in the driver's headrest, as shown in Figure 5a. To assess the equalization performance of the proposed approach in a different environment we have measured the impulse responses of another car, a Jeep Renegade and measured the impulse responses at multiple listening points. Its cabin response has been measured using \(\mathcal{M}=4\) omnidirectional microphone, one per seat. Three additional microphones have been mounted around microphone M2 for proximity tests, to assess the effect of head movements on the equalization performance. These microphones, labeled as PM1, PM2 and PM3 are placed at a distance of 6.5 cm (forward), 6.5 cm (backward) and 22.5 cm (lateral), respectively. For a one-ot-one comparison with the binaural tests done on the Giulia, a binaural mannequin was also mounted at the driver seat to capture binaural impulse responses. The sine sweep method has been used as well, in this case sampling at 48 kHz using an Audio Precision APX-586 analyzer and a Crown D-75A power amplifier to drive the loudspeakers. The Renegade loudspeakers are located in the car dashboard, on the four doors and a subwoofer is placed in the trunk. The baseline methods have been implemented in _Matlab_ ([[https://mathworks.com/products/matlab.html](https://mathworks.com/products/matlab.html)]([https://mathworks.com/products/matlab.html](https://mathworks.com/products/matlab.html))), while the proposed methods have been implemented in Python using _Keras_ ([[https://keras.io/](https://keras.io/)]([https://keras.io/](https://keras.io/))) with _Tensorflow_ ([[https://www.tensorflow.org/](https://www.tensorflow.org/)]([https://www.tensorflow.org/](https://www.tensorflow.org/))) as backend. They have been executed on a machine with Intel Core i7-4930K 3.40 GHz clock processor, 32 GB of RAM and Nvidia GTX-Titan GPU with 12 GB of dedicated RAM. The results are provided in terms of the mean square error (MSE) and average standard deviation \(\overline{\sigma}\). The MSE of the magnitude response is calculated bin-by-bin for each microphone between the desired frequency response and the measured magnitude frequency response. The results are averaged between all microphones, that is,:  
\[\overline{MSE}=\frac{1}{\mathcal{M}}\sum_{m=1}^{\mathcal{M}}\left(\frac{\sum_{ \omega_{i}=\omega_{l}}^{\omega_{h}}\left(|Y_{m}(\omega)|-|Y_{des}(\omega)| \right)^{2}}{\omega_{h}-\omega_{l}}\right). \tag{16}\]  
The average standard deviation \(\overline{\sigma}\) is calculated as:  
Figure 5: Top view of the Alfa Romeo Giulia (**a**) and the Jeep Renegade (**b**) showing the placement of the \(\mathcal{S}\) loudspeakers and the \(\mathcal{M}\) microphones. D indicates the dummy head. The three yellow labels around M2 are the proximity test microphone PM1, PM2, PM3.