# Influence of the Quality of Consumer Headphones in the Perception of Spatial Audio
## 6 Test 4. Frequency Response about Azimuth Localization
### Results  
A Cronbach's alpha analysis over the answers has been performed giving a value of \(\alpha=0.982\), which shows a high internal consistency.  
A one-way ANOVA showed a significant influence between the headphones and the deviation of the answered angle (deviation = answered angle-real angle) (\(F=2.399\); df = 8; \(p=0.014\)).  
A first exploration of the participants' answers reveals that several front-back confusions [26; 27] occur. For this reason, an evaluation of the amount of front-back confusions was performed for each of the headphones simulated. An ANOVA showed that there is a very significant influence of the type of headphones on the number of front-back confusions (\(F=46.307\); df = 8; \(p<0.001\)). In Figure 9, we can see that headphones (f)-AirL and (h)-LCmul2 produce an average of nearly 50% of front-back confusions. This can be logical, as both headphones are supposed to be in the low quality range. However, the (c)-MQcl headphone stands out in the group of high quality ones, as it has 30.2% of front-back confusions, more confusions than the (e)-LCmul headphone, with a significant difference. A comparison of the frequency response of the headphones that produce more front-back confusions ((f)-AirL, (h)-LCmul2 and (c)-MQcl) reveals that they share in common strong irregularities in the band of 100 to 1600 Hz. On the other side, other headphones of medium and low quality ranges that have less front-back confusions do not present these strong irregularities in that four-octave band. Because of that, we suspect this can be an affecting factor disturbing the front-back discrimination.  
There is no significant influence of the type of sound crossed with the headphones. The sound guitar is the only one that produces slightly less front-back confusions for all of the headphones.  
Due to the strong front-back confusion, the analysis of the deviation of the perceived sound with respect to the reproduced sound will produce large angle errors with complicated analysis of the results. A front-back confusion produces a bigger error for sources in the median plane than lateral sources, avoiding an analysis of the deviation angle (perceived angle-reproduced angle) with respect to the source position.  
Figure 9: Percentage of front-back confusions for the reference, headphones and the anchor.  
To overcome this setback, we propose a modified analysis of the error consisting of a preprocessing of the listener responses based on reflecting to the correct semi-plane the ones that have front-back confusion, leaving untouched the ones that do not. This correction eliminates big jumps in the deviation, focusing the experiment in the performance analysis of the headphones reproducing correctly the main spatial cues as ITD and the low frequency part of Interaural Level Difference (ILD). The high frequency part is more related to the pinna effect that is not considered with the reflection applied.  
Taking into account the strong front-back confusion, the analysis of the answer deviation from the reproduction angle of the sound was performed introducing the correction of the front-back confusion. Therefore, a symmetric image of the responses in the back (90\({}^{\circ}\) to 270\({}^{\circ}\)) is brought to the front.  
Figure 10 shows the deviation angle of the answers for the reproduction angle of the sounds, both of them front-back corrected. We can see that the deviations are quite uniform across the different headphones, except for the angles 90\({}^{\circ}\) and 270\({}^{\circ}\) in the cases of (f)-AirL and (h)-LCmu12. Looking at Figure 2, it is easy to see that the frequency responses of these two headphones present irregularities and deep level drops between 4 and 7 kHz. It is noticeable that the anchor LPF 7-kHz sounds auralized in the different angles (ANC1) are not affected by this problem, supporting the suspicion that the commented band is important for sources located in lateral positions.