## 5 Results
### Accuracy: SGE3 and NSGE3
Note that the largest errors of the validation set for SGE3 and NGE3 did not occur with the same command gain settings (see Figures 10 and 11). However, both of the cases had similar local setting of the command gains, where two adjacent high-frequency commands had the same value of +12 dB, and the command gain prior to these had a low negative value, creating a steep slope in the magnitude response. Furthermore, both errors occurred between these two command gain points instead of at the command gain frequency. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Design Method** &
\begin{tabular}{c} **Error at Commands Points \({}^{*}\)** \\ **Max** \\ \end{tabular} \\ \hline ACGE3 [3] & 0.97 dB & 0.53 dB \\ NGEQ3 [20] & 1.05 dB & 0.54 dB \\ SGE3(Proposed, WLS design) & **0.81 dB** & **0.50 dB** \\ NGE3 (Proposed, neural network) & 0.86 dB & **0.50 dB** \\ \hline \hline \end{tabular} \({}^{*}\) When two neighboring command gains were the same, the error was also measured in the frequency range between the command points.  
\end{table} 
Table 5: Comparison of magnitude-response accuracy in 10,000 random gain settings: third-octave design. The smallest errors in each column are emphasized. Figure 11: Example design using the proposed SGE3 and NSGE3 methods. With these command gain settings, included in a random set of 10,000 configurations, NSGE3 has its largest error of the entire validation set occurring between the two highest command points 10 kHz and 12.7 Hz, which have the same command gain of 12 dB. Figure 10: Example design using the proposed SGE3 and NSGE3 methods. With these command gains, SGE3 has its largest error of the entire validation set occurring between two high-frequency command points, 16 kHz and 20 kHz, which have the same command gain of 12 dB. The largest error of NSGE3, in this case, is smaller than that of SGE3. Table 6 shows the results of the magnitude-response accuracy experiment when using a validation dataset of 10,000 random command gain settings, with the same error criteria as was used with the third-octave case before. Table 6 shows the maximum error and the mean of 10,000 error maxima for SGEB and NSGEB. The maximum error was seen to be approximately 1.3 dB for both methods, whereas the mean performance error was about 0.6 dB. In fact, the trained neural network could estimate the filter gains in the validation dataset with high accuracy, which produced magnitude errors that were only 0.06 dB (maximum) and 0.01 dB (mean maximum) larger than the WLS-optimized filter gains used to train the neural network. Figures 14-16 illustrate the performance of the proposed Bark based GEQs via the magnitude responses of SGEB (- -) and NSGEB (--) and the optimized EQ filter gains (\(\square\) and \(\times\)) that were calculated based on the user-set command gains (\(\circ\)). Figure 14 shows the command gain settings that produced the largest error from the entire validation dataset. This time, the same command gain settings caused the largest errors for both SGEB and NSGEB, which were 1.26 and 1.32 dB, respectively. The largest errors occurred between the second and third command gain frequencies at 157 Hz, when their command gains were set to \(+12\) dB. These types of command gain settings at the lowest command points seemed to cause the maximum errors with the Bark based GEQs. This was due \begin{table}
\begin{tabular}{l c c} \hline \hline
**Design Method** & **Error at Commands Points \({}^{*}\)** \\  & **Max** & **Mean Max** \\ \hline SGEB (Iterative WLS design) & **1.26 dB** & **0.60 dB** \\ NSGEB (Neural network) & 1.32 dB & 0.61 dB \\ \hline \hline \end{tabular} \({}^{*}\) When two neighboring command gains were the same, the error was also measured in the frequency range between the command points.  
\end{table} 
Table 6: Comparison of the magnitude-response error in 10,000 random gain settings: Bark band design. The smallest error in each column is emphasized.