# An Audio Distortion Dynamic Range Index for Evaluating the Performance of Audio Systems
## 5 Discussion  
Comparing the proposed ADDR index with the SNR and SINAD indexes from the aspect of calculation method based on the spectrum, we can find that the existing indexes are equivalent to a fixed ADDR performance line, and the proposed ADDR plot is equivalent to connecting all the ADDR performance lines into a performance surface. Furthermore, the lifelike audio signals are generally nonstationary. For an audio DUT, the performance surface probably changes with the amplitude of the input signal. Therefore, a more practical and targeted comparison extends the proposed method from the two-dimensional area comparison to three-dimensional volume comparison, as is shown in Figure 10.  
The volume comparison is conducted on the ADDR performance body formed by the ADDR plot performance surface as a function of the amplitude of the input signal. Similarly, a smaller volume corresponding to better overall performance. At the same time, the ratio of each amplitude of the actual audio signal specified length in the time domain should be analyzed, and then the corresponding performance surface constituting the ADDR performance body should be weighted using this ratio. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**NoiseType** & **Attenuator (dB)** & **DUT** & **WER (\%)** & \(\Delta\) (\%)** & **Match?** \\ \hline \multirow{8}{*}{white} & \multirow{2}{*}{9} & 5 & 44.44 & \multirow{2}{*}{\(-0.58\)} & \multirow{2}{*}{\(\times\)} \\ \cline{3-5}  & & 6 & 43.86 & & \\ \cline{3-5}  & \multirow{2}{*}{12} & 5 & 32.16 & \multirow{2}{*}{\(1.17\)} & \multirow{2}{*}{\(\surd\)} \\ \cline{3-5}  & & 6 & 33.33 & & \\ \cline{3-5}  & \multirow{2}{*}{18} & 5 & 22.22 & \multirow{2}{*}{\(-0.58\)} & \multirow{2}{*}{\(\times\)} \\ \cline{3-5}  & & 6 & 21.64 & & \\ \cline{3-5}  & \multirow{2}{*}{35} & 5 & 19.3 & & \\ \cline{3-5}  & & 6 & 18.13 & & \\ \hline \multirow{8}{*}{babble} & \multirow{2}{*}{9} & 5 & 38.6 & \multirow{2}{*}{\(1.75\)} & \multirow{2}{*}{\(\surd\)} \\ \cline{3-5}  & & 6 & 40.35 & & \\ \cline{3-5}  & \multirow{2}{*}{12} & 5 & 25.15 & & \\ \cline{3-5}  & & 6 & 26.32 & & \\ \cline{3-5}  & \multirow{2}{*}{18} & 5 & 15.79 & & \\ \cline{3-5}  & & 6 & 19.3 & & \\ \cline{3-5}  & \multirow{2}{*}{35} & 5 & 15.79 & & \\ \cline{3-5}  & & 6 & 16.96 & & \\ \hline \multirow{8}{*}{factory1} & \multirow{2}{*}{9} & 5 & 40.35 & \multirow{2}{*}{\(2.34\)} & \multirow{2}{*}{\(\surd\)} \\ \cline{3-5}  & & 6 & 42.69 & & \\ \cline{3-5}  & \multirow{2}{*}{12} & 5 & 29.82 & & \\ \cline{3-5}  & & 6 & 31.58 & & \\ \cline{3-5}  & \multirow{2}{*}{18} & 5 & 20.47 & & \\ \cline{3-5}  & & 6 & 20.47 & & \\ \cline{3-5}  & \multirow{2}{*}{35} & 5 & 17.54 & & \\ \cline{3-5}  & & 6 & 17.54 & & \\ \hline \multicolumn{5}{c}{Averaged:} & 27.24 & 0.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Word error rate (WER) comparison of test utterances distorted by DUTs in situation B. Representing the proposed ADDR metric by a single number (quantifying the area in the ADDR-vs-threshold plot between the two reference lines and the plot-line) may be more useful. One possible idea is to set an absolute area that big enough to cover all the performance of practical audio systems on the output spectrum of the DUT, and then calculate the ratio of the area of the selected ADDR graph to that absolute area. The result will be between 0 to 1, and a value closer to 0 represents better performance. The ADDR index may have a certain supplementary effect on the RF systems compared with the existing indexes. This is because the RF systems also have a certain working bandwidth, all the harmonic, spurious and noise components are the reasons of performance degradation. In addition to the existing indexes such as SFDR, ADDR may also comprehensively reflect the effects of distorted spectral components on RF systems.