# An Audio Distortion Dynamic Range Index for Evaluating the Performance of Audio Systems
## 4 Simulation
### Performance Comparison of DUTs with Small difference of Different Existing Indexes  
Figure 8a,b shows the averaged spectrum of DUTs, which have the advantage of different existing indexes. It can be seen that the SNR of DUT5 has an advantage of 2.05 dB than DUT6 while the SINAD and THD of DUT6 have advantages of 2.27 dB and 2.72 dB than DUT5 respectively. In this situation, it is relatively more difficult to distinguish the performance difference of the two DUTs according to the existing indexes.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**NoiseType** & **Attenuator (dB)** & **DUT** & **WER (\%)** & \(\Delta\) (\%)** & **Match?** \\ \hline \multirow{6}{*}{white} & \multirow{2}{*}{9} & 3 & 57.31 & \multirow{2}{*}{0.00} & \multirow{2}{*}{-} \\ \cline{3-5}  & & 4 & 57.31 & & \\ \cline{3-5}  & & 3 & 44.44 & & \\ \cline{3-5}  & & 4 & 50.88 & & \\ \cline{3-5}  & & 3 & 33.33 & & \\ \cline{3-5}  & & 4 & 38.01 & & \\ \cline{3-5}  & & 3 & 28.07 & & \\ \cline{3-5}  & & 4 & 31.58 & & \\ \hline \multirow{6}{*}{babble} & \multirow{2}{*}{9} & 3 & 56.76 & \multirow{2}{*}{7.57} & \multirow{2}{*}{\(\surd\)} \\ \cline{3-5}  & & 4 & 64.33 & & \\ \cline{3-5}  & & 3 & 45.61 & & \\ \cline{3-5}  & & 4 & 46.78 & & \\ \cline{3-5}  & & 18 & 3 & 31.58 & & \\ \cline{3-5}  & & 4 & 35.67 & & \\ \cline{3-5}  & & 3 & 27.49 & & \\ \cline{3-5}  & & 4 & 32.16 & & \\ \hline \multirow{6}{*}{factory1} & \multirow{2}{*}{9} & 3 & 55.56 & \multirow{2}{*}{12.86} & \multirow{2}{*}{\(\surd\)} \\ \cline{3-5}  & & 4 & 68.42 & & \\ \cline{3-5}  & & 3 & 39.77 & & \\ \cline{3-5}  & & 4 & 47.37 & & \\ \cline{3-5}  & & 18 & 3 & 32.16 & & \\ \cline{3-5}  & & 4 & 36.26 & & \\ \cline{3-5}  & & 3 & 28.07 & & \\ \cline{3-5}  & & 4 & 32.75 & & \\ \hline \multicolumn{5}{c}{Averaged:} & 42.57 & 5.11 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Word error rate (WER) comparison of test utterances distorted by DUTs in situation A.  
The ADDR plots of the two DUTs are shown in Figure 9. In the ADDR plot, the left and right sides of the intersection of two curves indicate that these two DUTs each have their own performance advantages. However, the area of the specified region of DUT5 is smaller than that of DUT6. Base on the judgement rules and the area comparison method in Section II, Subsection B, the performance of DUT5 is better than DUT6 because the area 'S5' is smaller than 'S6'.  
From Table 3, it can be seen that the averaged WERs of these DUTs is about 27.24%, and the WERs of DUT2 are on average 0.88% higher than that of DUT5. This difference accounts for 0.88/27.24 \(\times\) 100% = 3.23%. The difference is relatively much smaller, which means these DUTs have very close overall performances. There are three '\(\times\)' symbols in Table, which represent the contrary results with the conclusion of ADDR. But it should be noted that these three negative values are relatively smaller, and a positive averaged WER of 0.88% and relatively many '\(\surd\)' symbols verify the conclusion obtained by the ADDR plots to a certain extent.  
In summary, the ADDR index can compare the performance of a DUT with a relatively high accuracy under some complicated comparison conditions. Therefore, it is an effective supplement to the existing indexes in some practical conditions.  
Figure 8: Output spectrum of DUT in situation B. (**a**) DUT5. (**b**) DUT6. Test signal: 996.1 Hz, 2 VPP; Band: DC-20 kHz; Sampling frequency: 40 kHz; Sampling points: 2048; Spectrum averaged times: 100; Kaiser window (\(\beta=0\)).  
Figure 9: ADDR plots of DUT5 and DUT6 in situation B.