## 5 Evaluation of the Auralization System
### Spatial Analysis  
In the previous section, the auralization system was evaluated in terms of its accuracy in reconstructing the acoustic pressure at different reference locations. Although this provides useful insight into the performance of the method, it does not give any information about the spatial characteristics of the synthesized sound field. This aspect was investigated by assessing the ability of the system to accurately reconstruct the zero and first order terms in the spherical harmonic expansion of the sound field, as described by Equation (4), often referred to as Ambisonics B-format signals. An accurate reconstruction of the zero and first order sound fields at the listening position implies an accurate reproduction of binaural localization cues at low frequencies [33]. Nevertheless, this approach is a preliminary analysis, and further investigation is required.  
The B-format reference signals were estimated by the implementation of an inverse method according the formulation proposed by the authors [34]. For this, virtual microphone arrays were used to sample the FE data at the positions where the B-format signals were intended to be synthesized. The B-format signals from the auralization system were obtained by recording the output of the rotation module (see Figure 15), which is based on a spherical harmonic transformation. The zero and first order components were recorded and compared to the numerical references.  
The B-format consists of four signals, which correspond to an omnidirectional (zero order) and three orthogonal dipoles (first order). They are refereed to in the Ambisonics literature as \(W\), \(X\), \(Y\) and \(Z\), respectively. The analysis of the B-format signals was carried out at Receivers 2 and 5. These were chosen because they corresponded to the locations where the best and worst agreement was found in terms of the mean errors for the monaural evaluation. The frequency responses in the narrow band and in the 1/3 octave band resolution of the reference and synthesized B-format signals are illustrated in Figures 25-32. A summary of the mean errors according to the B-format component is presented in Table 3.  
Figure 26: Comparison of full (**a**) and 1/3 octave band (**b**) frequency responses. Translated PWE (\(X\)) and reference (\(X\)) at translated Position 2.  
Figure 25: Comparison of full (**a**) and 1/3 octave band (**b**) frequency responses. Translated PWE (\(W\)) and reference (\(W\)) at translated Position 2.  
Figure 28: Comparison of full (**a**) and 1/3 octave band (**b**) frequency responses. Translated PWE (\(Z\)) and reference (\(Z\)) at translated Position 2.  
Figure 30: Comparison of full (**a**) and 1/3 octave band (**b**) frequency responses. Translated PWE (\(X\)) and reference (\(X\)) at translated Position 5.  
Figure 27: Comparison of full (**a**) and 1/3 octave band (**b**) frequency responses. Translated PWE (\(Y\)) and reference (\(Y\)) at translated Position 2.  
A comparison of the mean errors indicates that the field at Receiver 2 has smaller errors values than at Receiver 5. This is expected as the distance to the central point of the expansion of Receiver 2 is smaller. Regarding the B-format signals, the outcomes show that the reconstruction is more accurately performed for the \(W\) signals. In this case, a very good agreement between the frequency response synthesized by the auralization system and the reference signal was found up to the frequency established by Equation (14). For the remaining coefficients, the match is not as good as the zero order, but with good agreement in terms of the envelope of the frequency response.