# Particle-Velocity-Based Mixed-Source Sound Field Translation for Binaural Reproduction
## 6 Experimental Verification
### Experimental Methodology  
To generate the binaural test signals, we construct a virtual experimental environment, where there is a 4 th order receiver located at the origin and a free-field point source located at \((1,0,0)\) m, with respect to the origin. The receiver region is a spherical region with a radius of 0.042 m, to represent the spatial abilities of common spherical microphone arrays. We assume the microphone array works ideally, and the theoretical pressure coefficients (34) can be extracted from the ideal microphone recording. The parameters of the mixed-source model are the same as those in Section 5.1. We reproduce the sound image for the listener away from the recording area by extrapolation using the proposed method. The listener faces the positive \(x\)-axis, and the listener's head is aligned vertically with the point source on the \(x\)-\(y\) plane. We used the HRTFs of the FABIAN head and torso simulator [65] from the HUTUBS dataset [66; 67]. The source signal is a clip of dry instrumental music with 10 s duration and its spectrum energy mainly distributes in the frequency band below 8 kHz. We process the signals at a frame size of 4096 with 50% overlap and a 16 kHz sampling frequency. We carry out a MUSHRA [68] experiment to compare four translation methods; therefore, for a translated position there are a total of six binaural test signals in this experiment:  
* Reference/Hidden reference: The ground truth, which is obtained directly from filtering the theoretical point source signal with the HRTFs. * Anchor: Signals of the truncated recording at the origin, which are simulated using the pressure coefficients up to order \(N\) in (34). No translation is processed, but is filtered by the HRTFs. * P-CFS: Signals reconstructed using the closed-form solution of the sound-pressure-based expansion and rendered by the HRTFs. * V-LSS: Signals reconstructed using the least squares solution of the particle-velocity-based expansion and rendered by the HRTFs. * P-SS: Signals reconstructed using the sparse solution of the sound-pressure-based expansion and rendered by the HRTFs. * V-SS: Signals reconstructed using the sparse solution of the particle-velocity-based expansion and rendered by the HRTFs. We generate the above binaural test signals at six different translated positions outside the receiver region. All the translated positions are on the \(x\)-\(y\) plane, and they are \((0,1,0)\) m, \((0,-1,0)\) m, \((0,5,0.8,0)\) m, \((0.5,-0.8,0)\) m, \((1,1,0)\) m, and \((1,-1,0)\) m, respectively. In total, the scores of 31 subjects (16 females and 15 males) with normal hearing are collected for this listening experiment. Among the participants there are 14 experienced listeners with an audio research background and 17 common listeners without any audio research background. A random set out of the six sets of test signals is selected for each hearing subject. The test signals are played on a computer and the hearing subjects need to wear headphones to listen to the test signals. We provide the participants with Matlab programs containing the test signals with a user interface, and guide them to perform the experiment using their own computer and headphone through online meetings. The experiment includes two tests, and they are the source localization test and the basic audio quality test, respectively. The order in which the test signals are played is also random for each test. For the source localization test, the hearing subjects are asked to score all the test signals against the reference for the perceived direction of the sound source, whereas the hearing subjects need to score on the spectral distortions and other audible processing artifacts with respect to the reference for the basic audio quality test. During the test, the participants can arbitrarily switch between different test signals, and the duration of the experiment is usually within 20 min. The score ranges from 0 to 100.