# Upmix B-Format Ambisonic Room Impulse Responses Using a Generative Model
## 3 Upmixing Ambisonics Sound Field
### HiFi-Gan  
The Ambisonics sound field upmixing approach discussed in this paper addresses the challenges posed by the low spatial resolution and limited bandwidth of FOA RIRs. To overcome these limitations, HiFi-GAN is employed to model the lower-order RIRs in the time domain, which learns a function that maps the FOA to a higher-order counterpart. In this paper, Eigenmike is used as the acquisition device for capturing higher-order sound fields. However, it is worth noting that the proposed models can be extended to handle sound fields of an arbitrary order acquired by other types of microphone arrays. This flexibility allows for upmixing ARIRs to various orders, provided suitable training data are available. We use the first-order SH coefficients of signals recorded by Eigenmike or simulated at Eigenmike configuration as the lower-order ARIRs during the training phase. To align with the Eigenmike configuration, 32-channel signals are reconstructed from the measured or simulated FOA signals, which exclusively contain the first-order sound field information, and are utilized as inputs to the models. The HiFi-GAN network was initially proposed as an efficient and high-quality speech synthesis network [26; 30]. Here, it is used to generate the 32-channel microphone signals, i.e., the upmixed RIRs in this work. The discriminator of this network introduces the multi-scale discriminator (MSD) and STFT discriminator to enhance the discriminative capability between synthetic and real signals. The generator module consists of an upsampling structure and employs Multi-Receptive Field Fusion (MRF). In this study, a network structure similar to that of [27] is used to model the time domain FOA RIRs. The schematic diagram of HiFi-GAN is depicted in Figure 3, illustrating the overall structure of the model. The network architecture of the generator and discriminators in HiFi-GAN is described as follows. 1. Generator G  
The generator G in the HiFi-GAN architecture consists of a 1D convolution layer, a 30-layer feed-forward WaveNet [31; 32], and a postnet module [26]. The feed-forward WaveNet utilizes dilated convolutions with a kernel size of 3 and exponentially increasing dilation factors ranging from 1 to 512. This design yields a receptive field that is exponential in the number of layers. Each dilated convolution is embedded within a residual layer that includes an additional \(1\times 1\) convolution and a residual connection. The contribution of the Tanh activation function in each layer is controlled by sigmoidal gates. The following postnet module consists of twelve stacks of 1D-convolutional layer and batch normalization. Each convolution layer has 128 channels and a kernel length of 32. The activation function used in the postnet is Tanh. The architecture of the generator is shown in Figure 4.  
Figure 3: The schematic diagram of HiFi-GAN includes the MSD with three Waveform Discriminators [26], as well as an STFT discriminator. 2. MSD To effectively capture both the fine and coarse structures of the generated data, the MSD utilizes average pooling at various scales on the input signals prior to feeding them into the convolutional layers of the discriminator. The design of the MSD framework draws inspiration from the architecture proposed in [26], which incorporates three sub-discriminators operating at different scales: the original data and two scale-averaged pooling operations (\(\times 2\) and \(\times 4\) average pooling). Each sub-discriminator consists of strided convolutional blocks, each comprising six 1D convolutional layers with Leaky ReLU activation. 3. STFT Discriminator The STFT discriminator is designed to capture the time-frequency characteristics of the input signals by performing an STFT on the input signal, following the approach proposed in [33]. The STFT window length is set to 2048, with a hop size set to half the window length. The network architecture of the STFT discriminator comprises four stacks of 2D convolutional layers, along with batch normalization and a Gated Linear Unit (GLU).