# An Audio Distortion Dynamic Range Index for Evaluating the Performance of Audio Systems
## 2 Definition of the New Index
### Judgement Rules  
Taking the comparison of two DUTs as an example, the ADDR plots of these DUTs are illustrated in Figure 2a. There are two basic rules: (a) Corresponding to the same ADDR on the vertical axis, the smaller the value of the threshold on the horizontal axis is, the better the DUT performance is. This is reasonable because for a same ratio of signal to specified distorted spectral components, a lower threshold represents a larger clearance area near the fundamental signal. (b) Corresponding to a same threshold on the horizontal axis, the larger the value of the ADDR on the vertical axis is, the better the DUT performance is. Because for the same threshold a higher ADDR value represents a larger ratio of signal to specified distorted spectral components.  
The ADDR plot reflects the process of performance variation from SINAD to DR caused by the distorted components of a DUT. Therefore, comparing the ADDR performance of two DUTs is achieved by comparing the area of the specified region of the ADDR plot. The smaller the area of the specified region of a DUT is, the better the performance of the DUT will be. The steps to obtain the area of the specified region are as follows, and they are correspond to each sub-figure in Figure 2 respectively.  
Step 1: Put the ADDR plots of the two DUTs in a figure;  
Step 2: Specify the origin of the specified region as the intersection of the horizontal reference line whose vertical position is the biggest ADDR value and the vertical reference line whose horizontal position is the smallest threshold;  
Step 3: Draw three reference lines. Start from the origin, draw a horizontal reference line and a vertical reference line to left and to down respectively. Draw a vertical reference line whose horizontal position corresponds to the biggest threshold of these DUTs;  
Step 4: The area of the specified area is equal to the area formed after the ADDR curve directly intersects or projects its ends onto the reference lines.  
Projecting the ADDR curve's ends onto the reference lines is necessary because it prevents the area comparison rule from producing incorrect results based on the two basic rules in some cases and provide more flexibility.  
Figure 2: (a) Step1, (b) Step 2, (c) Step 3 and (d) Step 4 of obtaining the area of the specified region of the ADDR plot for comparing the performance of two DUTs.  
For the DUTs with different maximum thresholds, projecting onto the right vertical reference line is equivalent to horizontally extending the ADDR plot of the corresponding DUT with a smaller minimum threshold in that direction. This is reasonable because in the spectrum if the position of the threshold is higher than the maximum of distorted components, the ADDR result is unchanged. The projection onto the left vertical reference line is to make the comparison process meet the set rules.  
Figure 2d shows the comparison result, within which the reference lines are illustrated by the black lines. The origin is shown as the dot on the north-western region. The areas of the specified region of DUT1 and DUT2 are illustrated by the areas of 'S1' and 'S2', respectively. It is obvious that the area 'S1' is smaller than the area 'S2', thus, the overall ADDR performance of DUT1 is better than that of DUT2.