# Upmix B-Format Ambisonic Room Impulse Responses Using a Generative Model
## 5 Experiments Results
### Sound Field Reconstruction Error  
In this subsection, we conduct an in-depth analysis and comparison of the spatial and frequency domain characteristics of the upmixed RIRs using the ASDM method and the proposed HiFi-GAN method, in comparison with RIRs obtained through the Ambison encoding of the original FOA recordings. This analysis extends to various frequency points beyond the aliasing frequency. The colorbar displayed in Figure 6 within the figure represents values in decibels (dB). Figure 5: Comparison of (**a**) the room impulse responses and (**b**) the spectrum of RIRs obtained from four scenarios: upmixed RIRs using HiFi-GAN, upmixed RIRs using ASDM, results of FOA reconstruction, and the ground truth RIRs. Figure 6: The spatial responses at different frequency points above the 1 st-order aliasing frequency on the sphere for the four scenarios: (**a**) The ground truth. (**b**) The upmixed RIRs using HiFi-GAN. (**c**) The upmixed RIRs using ASDM. (**d**) The results of FOA reconstruction. Given that the spherical array RIRs contain sound field information specific to their respective locations, we first perform a visual analysis of the spatial responses at various frequency points across the sphere for four distinct signals, including the first-order RIRs, the upmixed RIRs using the HiFi-GAN model, the upmixed RIRs using the ASDM method, and the ground truth RIRs. For evaluation purposes, we specifically select the center frequency of the one-third octave band above the aliasing frequency. In Figure 6, the spatial aliasing artifacts appear as the frequency exceeds the first-order aliasing frequency (1.2 kHz), accompanied by a noticeable roll-off in the FOA spectrum with increasing frequency. Although the upmixed RIRs using HiFi-GAN may exhibit slight variations in amplitude spectrum compared to the ground truth, they effectively preserve more accurate spatial information. It shows the effective upmixing capabilities of the HiFi-GAN model, which enhances both the spatial and spectral characteristics. Certainly, ASDM enhances the sound pressure in a specific direction, thereby sharpening the directional characteristics of the original RIRs. However, it is important to note that ASDM also is subject to certain limitations, such as DOA estimation error. Given the assumption that each time window contains waves from a single direction, the RIRs generated through the ASDM process might not fully capture the spatial and spectral intricacies of the actual, ground truth signals. When conducting quantitative analysis to evaluate spectral errors, we exclude the ASDM method from consideration. This is due to the specific equalization process employed by ASDM, which is designed to align the spectral characteristics with the FOA signals. As a result, it has significantly larger errors when representing the high-frequency spectral components of the HOA signals. Figure 7 illustrates the NMSE values average across the 32-channel of a specific test set, which are averaged over one-third octave bands. Additionally, we calculated the NMSE separately for each channel within different test sets, and the results are presented in Figure 8. As shown in Figures 7 and 8, the normalized mean square error (NMSE) values for the RIRs upmixed by HiFi-GAN are much lower compared to the original FOA RIRs for frequencies above the aliasing cutoff. Figure 7 demonstrates a maximum improvement of approximately 3.6 dB in reconstruction accuracy achieved by the HiFi-GAN model over FOA. It is worth noting that although HiFi-GAN primarily focuses on modeling the time domain rather than directly modeling the amplitude spectrum, it exhibits remarkable upmixing performance. This can likely be attributed to the multiple discriminators that perform multi-scale discrimination and STFT discrimination in both the time and frequency domains. The collective guidance provided by these discriminators facilitates the effective learning of features related to higher-order Ambisonic signals by the HiFi-GAN generator model.